---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20865'
abstract:
- lang: eng
text: "We prove the convergence of a modified Jordan–Kinderlehrer–Otto scheme to
a solution\r\nto the Fokker–Planck equation in Ω e R^d with general—strictly positive
and temporally\r\nconstant—Dirichlet boundary conditions. We work under mild assumptions
on the domain,\r\nthe drift, and the initial datum. In the special case where
Ω is an interval in R1, we prove\r\nthat such a solution is a gradient flow—curve
of maximal slope—within a suitable space of\r\nmeasures, endowed with a modified
Wasserstein distance. Our discrete scheme and modified\r\ndistance draw inspiration
from contributions by A. Figalli and N. Gigli [J. Math. Pures\r\nAppl. 94, (2010),
pp. 107–130], and J. Morales [J. Math. Pures Appl. 112, (2018), pp. 41–88]\r\non
an optimal-transport approach to evolution equations with Dirichlet boundary conditions.\r\nSimilarly
to these works, we allow the mass to flow from/to the boundary ∂Ω throughout\r\nthe
evolution. However, our leading idea is to also keep track of the mass at the
boundary\r\nby working with measures defined on the whole closure Ω . The driving
functional is a\r\nmodification of the classical relative entropy that also makes
use of the information at the\r\nboundary. As an intermediate result, when Ω is
an interval in R1, we find a formula for the\r\ndescending slope of this geodesically
nonconvex functional."
acknowledgement: The author would like to thank Jan Maas for suggesting this project
and for many helpful comments, Antonio Agresti, Lorenzo Dello Schiavo and Julian
Fischer for several fruitful discussions, Oliver Tse for pointing out the reference
[10], and the anonymous reviewer for carefully reading this manuscript and providing
valuable suggestions. He also gratefully acknowledges support from the Austrian
Science Fund (FWF) project 10.55776/F65.Open access funding provided by Institute
of Science and Technology (IST Austria).
article_number: '23'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Quattrocchi F. Variational structures for the Fokker-Planck equation with general
Dirichlet boundary conditions. Calculus of Variations and Partial Differential
Equations. 2026;65(1). doi:10.1007/s00526-025-03193-1
apa: Quattrocchi, F. (2026). Variational structures for the Fokker-Planck equation
with general Dirichlet boundary conditions. Calculus of Variations and Partial
Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-025-03193-1
chicago: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” Calculus of Variations and Partial
Differential Equations. Springer Nature, 2026. https://doi.org/10.1007/s00526-025-03193-1.
ieee: F. Quattrocchi, “Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions,” Calculus of Variations and Partial
Differential Equations, vol. 65, no. 1. Springer Nature, 2026.
ista: Quattrocchi F. 2026. Variational structures for the Fokker-Planck equation
with general Dirichlet boundary conditions. Calculus of Variations and Partial
Differential Equations. 65(1), 23.
mla: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” Calculus of Variations and Partial
Differential Equations, vol. 65, no. 1, 23, Springer Nature, 2026, doi:10.1007/s00526-025-03193-1.
short: F. Quattrocchi, Calculus of Variations and Partial Differential Equations
65 (2026).
corr_author: '1'
date_created: 2025-12-29T12:06:26Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-04-07T08:37:46Z
day: '01'
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department:
- _id: JaMa
doi: 10.1007/s00526-025-03193-1
external_id:
arxiv:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Variational structures for the Fokker-Planck equation with general Dirichlet
boundary conditions
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abstract:
- lang: eng
text: "The Dean–Kawasaki equation—one of the most fundamental SPDEs of\r\nfluctuating
hydrodynamics—has been proposed as a model for density fluctuations in weakly
interacting particle systems. In its original form, it is highly\r\nsingular and
fails to be renormalizable, even by approaches such as regularity structures and
paracontrolled distributions, hindering mathematical approaches to its rigorous
justification. It has been understood recently that it is\r\nnatural to introduce
a suitable regularization, for example, by applying a formal spatial discretization
or by truncating high-frequency noise: This yields\r\nwell-posed equations that
should still precisely approximate the law of the\r\nparticle density fluctuations.\r\nIn
the present work, we prove that a regularization in the form of a formal\r\ndiscretization
of the Dean–Kawasaki equation indeed accurately describes\r\ndensity fluctuations
in systems of weakly interacting diffusing particles: We\r\nshow that, in suitable
weak metrics, the law of fluctuations as predicted by\r\nthe discretized Dean–Kawasaki
SPDE approximates the law of fluctuations\r\nof the original particle system,
up to an error that is of arbitrarily high order in\r\nthe inverse particle number
and a discretization error. In particular, the Dean–\r\nKawasaki equation provides
a means for efficient and accurate simulations of\r\ndensity fluctuations in weakly
interacting particle systems."
acknowledgement: All authors gratefully acknowledge funding from the Austrian Science
Fund (FWF) through the project F65. CR gratefully acknowledges support from the
Austrian Science Fund (FWF), grants P30000, P33010, W1245. FC gratefully acknowledges
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
last_name: Cornalba
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Jonas
full_name: Ingmanns, Jonas
id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
last_name: Ingmanns
orcid: 0009-0008-1310-7946
- first_name: Claudia
full_name: Raithel, Claudia
last_name: Raithel
citation:
ama: Cornalba F, Fischer JL, Ingmanns J, Raithel C. Density fluctuations in weakly
interacting particle systems via the Dean–Kawasaki equation. The Annals of
Probability. 2026;54(1):155-215. doi:10.1214/25-aop1763
apa: Cornalba, F., Fischer, J. L., Ingmanns, J., & Raithel, C. (2026). Density
fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation.
The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aop1763
chicago: Cornalba, Federico, Julian L Fischer, Jonas Ingmanns, and Claudia Raithel.
“Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki
Equation.” The Annals of Probability. Institute of Mathematical Statistics,
2026. https://doi.org/10.1214/25-aop1763.
ieee: F. Cornalba, J. L. Fischer, J. Ingmanns, and C. Raithel, “Density fluctuations
in weakly interacting particle systems via the Dean–Kawasaki equation,” The
Annals of Probability, vol. 54, no. 1. Institute of Mathematical Statistics,
pp. 155–215, 2026.
ista: Cornalba F, Fischer JL, Ingmanns J, Raithel C. 2026. Density fluctuations
in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals
of Probability. 54(1), 155–215.
mla: Cornalba, Federico, et al. “Density Fluctuations in Weakly Interacting Particle
Systems via the Dean–Kawasaki Equation.” The Annals of Probability, vol.
54, no. 1, Institute of Mathematical Statistics, 2026, pp. 155–215, doi:10.1214/25-aop1763.
short: F. Cornalba, J.L. Fischer, J. Ingmanns, C. Raithel, The Annals of Probability
54 (2026) 155–215.
corr_author: '1'
date_created: 2026-05-20T08:25:25Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-05-21T07:21:25Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1214/25-aop1763
ec_funded: 1
external_id:
arxiv:
- '2303.00429'
file:
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content_type: application/pdf
creator: dernst
date_created: 2026-05-21T07:11:27Z
date_updated: 2026-05-21T07:11:27Z
file_id: '21906'
file_name: 2026_AnnalsProbability_Cornalba.pdf
file_size: 865745
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success: 1
file_date_updated: 2026-05-21T07:11:27Z
has_accepted_license: '1'
intvolume: ' 54'
issue: '1'
keyword:
- Weakly interacting particle systems
- fluctuating hydrodynamics
- Dean-Kawasaki equation
- stochastic PDEs
- numerical approximation
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 155-215
project:
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call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: The Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki
equation
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_id: '21918'
acknowledged_ssus:
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acknowledgement: "At different stages of my PhD, my work was supported by several
grants: the\r\nDOC fellowship of the Austrian Academy of Sciences (26293, awarded
to me),\r\nthe FWF-SFB grant (PT1032F06504 n. F65, awarded to Jan Maas), and the
ERC\r\ngrant (PR1032ERC01 n. 716117, awarded to Jan Maas). I also appreciate the
help\r\nfrom the Scientific Computing unit for their advice on the cluster usage."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Kseniia
full_name: Khudiakova, Kseniia
id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
last_name: Khudiakova
orcid: 0000-0002-6246-1465
citation:
ama: Khudiakova K. How epistasis and purifying selection shape genetic diversity.
2026. doi:10.15479/AT-ISTA-21918
apa: Khudiakova, K. (2026). How epistasis and purifying selection shape genetic
diversity. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-21918
chicago: Khudiakova, Kseniia. “How Epistasis and Purifying Selection Shape Genetic
Diversity.” Institute of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-21918.
ieee: K. Khudiakova, “How epistasis and purifying selection shape genetic diversity,”
Institute of Science and Technology Austria, 2026.
ista: Khudiakova K. 2026. How epistasis and purifying selection shape genetic diversity.
Institute of Science and Technology Austria.
mla: Khudiakova, Kseniia. How Epistasis and Purifying Selection Shape Genetic
Diversity. Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-21918.
short: K. Khudiakova, How Epistasis and Purifying Selection Shape Genetic Diversity,
Institute of Science and Technology Austria, 2026.
corr_author: '1'
date_created: 2026-05-27T06:26:08Z
date_published: 2026-06-07T00:00:00Z
date_updated: 2026-06-12T12:43:35Z
day: '07'
ddc:
- '576'
degree_awarded: PhD
department:
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- _id: NiBa
- _id: JaMa
doi: 10.15479/AT-ISTA-21918
ec_funded: 1
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language:
- iso: eng
month: '06'
oa_version: Published Version
page: '89'
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8
grant_number: '26293'
name: The impact of deleterious mutations on small populations
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
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relation: part_of_dissertation
status: deleted
- id: '21967'
relation: part_of_dissertation
status: public
- id: '21968'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: How epistasis and purifying selection shape genetic diversity
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year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20814'
abstract:
- lang: eng
text: We characterize all semigroups sandwiched between the semigroup of a Dirichlet
form and the semigroup of its active main part. In case the Dirichlet form is
regular, we give a more explicit description of the quadratic forms of the sandwiched
semigroups in terms of pairs consisting of an open set and a measure on an abstract
boundary.
acknowledgement: "Open Access funding enabled and organized by Projekt DEAL. The first
three authors acknowledge financial support of the DFG within the priority programme
Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic
Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number
F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (grant
agreement No 716117)."
article_number: '6'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthias
full_name: Keller, Matthias
last_name: Keller
- first_name: Daniel
full_name: Lenz, Daniel
last_name: Lenz
- first_name: Marcel
full_name: Schmidt, Marcel
last_name: Schmidt
- first_name: Michael
full_name: Schwarz, Michael
last_name: Schwarz
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of
intermediate forms between a regular Dirichlet form and its active main part.
Potential Analysis. 2026;64(1). doi:10.1007/s11118-025-10251-y
apa: Keller, M., Lenz, D., Schmidt, M., Schwarz, M., & Wirth, M. (2026). Boundary
representations of intermediate forms between a regular Dirichlet form and its
active main part. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-025-10251-y
chicago: Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior
Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet
Form and Its Active Main Part.” Potential Analysis. Springer Nature, 2026.
https://doi.org/10.1007/s11118-025-10251-y.
ieee: M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations
of intermediate forms between a regular Dirichlet form and its active main part,”
Potential Analysis, vol. 64, no. 1. Springer Nature, 2026.
ista: Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2026. Boundary representations
of intermediate forms between a regular Dirichlet form and its active main part.
Potential Analysis. 64(1), 6.
mla: Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between
a Regular Dirichlet Form and Its Active Main Part.” Potential Analysis,
vol. 64, no. 1, 6, Springer Nature, 2026, doi:10.1007/s11118-025-10251-y.
short: M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis
64 (2026).
das_tickbox: '1'
dataavailabilitystatement: No datasets were generated or analysed during the current
study.
date_created: 2025-12-14T23:02:03Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-07-27T10:25:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-025-10251-y
ec_funded: 1
external_id:
arxiv:
- '2301.01035'
file:
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checksum: 9f5a4e900b8d4c74c6b5bf7c3bad54e1
content_type: application/pdf
creator: dernst
date_created: 2026-07-27T10:25:21Z
date_updated: 2026-07-27T10:25:21Z
file_id: '22414'
file_name: 2026_PotentialAnalysis_Keller.pdf
file_size: 445935
relation: main_file
success: 1
file_date_updated: 2026-07-27T10:25:21Z
has_accepted_license: '1'
intvolume: ' 64'
issue: '1'
keyword:
- Dirichlet forms
- Domination of semigroups
- Dirichlet
- Neumann and Robin boundary conditions
language:
- iso: eng
mathsc:
- 31C15
- 31C25
- 35A15
- 35J10
- 47D07
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Boundary representations of intermediate forms between a regular Dirichlet
form and its active main part
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '18706'
abstract:
- lang: eng
text: "We prove discrete-to-continuum convergence for dynamical optimal transport
on Zd\r\n -periodic graphs with cost functional having linear growth at infinity.
This result provides an answer to a problem left open by Gladbach, Kopfer, Maas,
and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the
convergence behaviour of discrete boundary-value dynamical transport problems
is proved under the stronger assumption of superlinear growth. Our result extends
the known literature to some important classes of examples, such as scaling limits
of 1 -Wasserstein transport problems. Similarly to what happens in the quadratic
case, the geometry of the graph plays a crucial role in the structure of the limit
cost function, as we discuss in the final part of this work, which includes some
visual representations."
acknowledgement: L.P. gratefully acknowledges fundings from the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1,
Projekt-ID 390685813. F.Q. gratefully acknowledges support from the Austrian Science
Fund (FWF) project 10.55776/F65.
article_processing_charge: Yes
article_type: original
author:
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Portinale L, Quattrocchi F. Discrete-to-continuum limits of optimal transport
with linear growth on periodic graphs. European Journal of Applied Mathematics.
2026;37(3):614-642. doi:10.1017/s0956792524000810
apa: Portinale, L., & Quattrocchi, F. (2026). Discrete-to-continuum limits of
optimal transport with linear growth on periodic graphs. European Journal of
Applied Mathematics. Cambridge University Press. https://doi.org/10.1017/s0956792524000810
chicago: Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits
of Optimal Transport with Linear Growth on Periodic Graphs.” European Journal
of Applied Mathematics. Cambridge University Press, 2026. https://doi.org/10.1017/s0956792524000810.
ieee: L. Portinale and F. Quattrocchi, “Discrete-to-continuum limits of optimal
transport with linear growth on periodic graphs,” European Journal of Applied
Mathematics, vol. 37, no. 3. Cambridge University Press, pp. 614–642, 2026.
ista: Portinale L, Quattrocchi F. 2026. Discrete-to-continuum limits of optimal
transport with linear growth on periodic graphs. European Journal of Applied Mathematics.
37(3), 614–642.
mla: Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits
of Optimal Transport with Linear Growth on Periodic Graphs.” European Journal
of Applied Mathematics, vol. 37, no. 3, Cambridge University Press, 2026,
pp. 614–42, doi:10.1017/s0956792524000810.
short: L. Portinale, F. Quattrocchi, European Journal of Applied Mathematics 37
(2026) 614–642.
das_tickbox: '0'
date_created: 2024-12-23T11:03:59Z
date_published: 2026-06-01T00:00:00Z
date_updated: 2026-08-07T22:31:04Z
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ddc:
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- _id: JaMa
doi: 10.1017/s0956792524000810
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success: 1
file_date_updated: 2026-07-23T05:55:03Z
has_accepted_license: '1'
intvolume: ' 37'
isi: 1
issue: '3'
keyword:
- optimal transport
- discrete-to-continuum
- homogenisation
- linear growth
- gamma-convergence
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 614-642
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: European Journal of Applied Mathematics
publication_identifier:
eissn:
- 1469-4425
issn:
- 0956-7925
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
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relation: dissertation_contains
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researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Discrete-to-continuum limits of optimal transport with linear growth on periodic
graphs
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18632'
abstract:
- lang: eng
text: 'For an arbitrary dimension (Formula presented.), we study: the polyharmonic
Gaussian field (Formula presented.) on the discrete torus (Formula presented.),
that is the random field whose law on (Formula presented.) given by (Formula presented.)
where (Formula presented.) is the Lebesgue measure and (Formula presented.) is
the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG)
measure associated with it, that is, the random measure on (Formula presented.)
(Formula presented.) where (Formula presented.) is a regularity parameter. As
(Formula presented.), we prove convergence of the fields (Formula presented.)
to the polyharmonic Gaussian field (Formula presented.) on the continuous torus
(Formula presented.), as well as convergence of the random measures (Formula presented.)
to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula
presented.). '
acknowledgement: "KTS is grateful to Christoph Thiele for valuable discussions and
helpful references. LDS is grateful to Nathanaël Berestycki for valuable discussions
on Gaussian Multiplicative Chaoses. The authors are grateful to an anonymous reviewer
for suggestions which improved the presentation.\r\nThe authors gratefully acknowledge
funding by the Deutsche Forschungsgemeinschaft through the project ‘Random Riemannian
Geometry’ within the SPP 2265 ‘Random Geometric Systems.'\r\nLDS gratefully acknowledges
financial support from the European Research Council (grant agreement No. 716117,
awarded to J. Maas) and from the Austrian Science Fund (FWF). His research was funded
by the Austrian Science Fund (FWF) project 10.55776/F65 and project 10.55776/ESP208.\r\nRH,
EK, and KTS gratefully acknowledge funding by the Hausdorff Center for Mathematics
(project ID 390685813), and through project B03 within the CRC 1060 (project ID
211504053). RH and KTS also gratefully acknowledges financial support from the European
Research Council through the ERC AdG ‘RicciBounds’ (grant agreement 694405).\r\nOpen
access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Ronan
full_name: Herry, Ronan
last_name: Herry
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: 'Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville
quantum gravity measures on tori of arbitrary dimension: From discrete to continuous.
Mathematische Nachrichten. 2025;298(1):244-281. doi:10.1002/mana.202400169'
apa: 'Dello Schiavo, L., Herry, R., Kopfer, E., & Sturm, K. T. (2025). Polyharmonic
fields and Liouville quantum gravity measures on tori of arbitrary dimension:
From discrete to continuous. Mathematische Nachrichten. Wiley. https://doi.org/10.1002/mana.202400169'
chicago: 'Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm.
“Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary
Dimension: From Discrete to Continuous.” Mathematische Nachrichten. Wiley,
2025. https://doi.org/10.1002/mana.202400169.'
ieee: 'L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields
and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete
to continuous,” Mathematische Nachrichten, vol. 298, no. 1. Wiley, pp.
244–281, 2025.'
ista: 'Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2025. Polyharmonic fields and
Liouville quantum gravity measures on tori of arbitrary dimension: From discrete
to continuous. Mathematische Nachrichten. 298(1), 244–281.'
mla: 'Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum
Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.”
Mathematische Nachrichten, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:10.1002/mana.202400169.'
short: L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten
298 (2025) 244–281.
date_created: 2024-12-08T23:01:56Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1002/mana.202400169
ec_funded: 1
external_id:
arxiv:
- '2302.02963'
isi:
- '001366948500001'
file:
- access_level: open_access
checksum: 1dc50d156feb777c86d779fb1c9ac875
content_type: application/pdf
creator: dernst
date_created: 2025-01-13T10:34:42Z
date_updated: 2025-01-13T10:34:42Z
file_id: '18838'
file_name: 2025_MathNachrichten_DelloSchiavo.pdf
file_size: 1734511
relation: main_file
success: 1
file_date_updated: 2025-01-13T10:34:42Z
has_accepted_license: '1'
intvolume: ' 298'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 244-281
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Mathematische Nachrichten
publication_identifier:
eissn:
- 1522-2616
issn:
- 0025-584X
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary
dimension: From discrete to continuous'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 298
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19027'
abstract:
- lang: eng
text: 'Stochastic PDEs of fluctuating hydrodynamics are a powerful tool for the
description of fluctuations in many-particle systems. In this paper, we develop
and analyze a multilevel Monte Carlo (MLMC) scheme for the Dean–Kawasaki equation,
a pivotal representative of this class of SPDEs. We prove analytically and demonstrate
numerically that our MLMC scheme provides a significant reduction in computational
cost (with respect to a standard Monte Carlo method) in the simulation of the
Dean–Kawasaki equation. Specifically, we link this reduction in cost to having
a sufficiently large average particle density and show that sizeable cost reductions
can be obtained even when we have solutions with regions of low density. Numerical
simulations are provided in the two-dimensional case, confirming our theoretical
predictions. Our results are formulated entirely in terms of the law of distributions
rather than in terms of strong spatial norms: this crucially allows for MLMC speed-ups
altogether despite the Dean–Kawasaki equation being highly singular.'
acknowledgement: The work of the authors was supported by the Austrian Science Fund
(FWF) projectF65.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Cornalba F, Fischer JL. Multilevel Monte Carlo methods for the Dean–Kawasaki
equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis.
2025;63(1):262-287. doi:10.1137/23M1617345
apa: Cornalba, F., & Fischer, J. L. (2025). Multilevel Monte Carlo methods for
the Dean–Kawasaki equation from fluctuating hydrodynamics. SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1617345
chicago: Cornalba, Federico, and Julian L Fischer. “Multilevel Monte Carlo Methods
for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” SIAM Journal
on Numerical Analysis. Society for Industrial and Applied Mathematics, 2025.
https://doi.org/10.1137/23M1617345.
ieee: F. Cornalba and J. L. Fischer, “Multilevel Monte Carlo methods for the Dean–Kawasaki
equation from fluctuating hydrodynamics,” SIAM Journal on Numerical Analysis,
vol. 63, no. 1. Society for Industrial and Applied Mathematics, pp. 262–287, 2025.
ista: Cornalba F, Fischer JL. 2025. Multilevel Monte Carlo methods for the Dean–Kawasaki
equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis. 63(1),
262–287.
mla: Cornalba, Federico, and Julian L. Fischer. “Multilevel Monte Carlo Methods
for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” SIAM Journal
on Numerical Analysis, vol. 63, no. 1, Society for Industrial and Applied
Mathematics, 2025, pp. 262–87, doi:10.1137/23M1617345.
short: F. Cornalba, J.L. Fischer, SIAM Journal on Numerical Analysis 63 (2025) 262–287.
corr_author: '1'
date_created: 2025-02-16T23:02:34Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-09-30T10:30:31Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/23M1617345
external_id:
arxiv:
- '2311.08872'
isi:
- '001447583400011'
file:
- access_level: open_access
checksum: 53505647e848ed50f7e0d00c369b14e7
content_type: application/pdf
creator: dernst
date_created: 2025-02-17T08:32:23Z
date_updated: 2025-02-17T08:32:23Z
file_id: '19029'
file_name: 2025_SIAMNumerAnaly_Cornalba.pdf
file_size: 2435019
relation: main_file
success: 1
file_date_updated: 2025-02-17T08:32:23Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 262-287
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: SIAM Journal on Numerical Analysis
publication_identifier:
eissn:
- 1095-7170
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating
hydrodynamics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 63
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20040'
abstract:
- lang: eng
text: 'Contractive coupling rates have been recently introduced by Conforti as a
tool to establish convex Sobolev inequalities (including modified log-Sobolev
and Poincaré inequality) for some classes of Markov chains. In this work, for
most of the examples discussed by Conforti, we use contractive coupling rates
to prove stronger inequalities, in the form of curvature lower bounds (in entropic
and discrete Bakry–Émery sense) and geodesic convexity of some entropic functionals.
In addition, we recall and give straightforward generalizations of some notions
of coarse Ricci curvature, and we discuss some of their properties and relations
with the concepts of couplings and coupling rates: as an application, we show
exponential contraction of the p-Wasserstein distance for the heat flow in the
aforementioned examples.'
acknowledgement: "The author warmly thanks Jan Maas for suggesting the project and
for his guidance, and Melchior Wirth and Haonan Zhang for useful discussions. The
author is also grateful to an anonymous reviewer for carefully reading the manuscript
and providing many valuable suggestions. The author gratefully acknowledges support
by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme\r\n(grant agreement No. 716117) and by the Austrian Science
Fund (FWF), Project SFB F65."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov
chains. The Annals of Applied Probability. 2025;35(1):196-250. doi:10.1214/24-aap2113
apa: Pedrotti, F. (2025). Contractive coupling rates and curvature lower bounds
for Markov chains. The Annals of Applied Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/24-aap2113
chicago: Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds
for Markov Chains.” The Annals of Applied Probability. Institute of Mathematical
Statistics, 2025. https://doi.org/10.1214/24-aap2113.
ieee: F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov
chains,” The Annals of Applied Probability, vol. 35, no. 1. Institute of
Mathematical Statistics, pp. 196–250, 2025.
ista: Pedrotti F. 2025. Contractive coupling rates and curvature lower bounds for
Markov chains. The Annals of Applied Probability. 35(1), 196–250.
mla: Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds
for Markov Chains.” The Annals of Applied Probability, vol. 35, no. 1,
Institute of Mathematical Statistics, 2025, pp. 196–250, doi:10.1214/24-aap2113.
short: F. Pedrotti, The Annals of Applied Probability 35 (2025) 196–250.
corr_author: '1'
date_created: 2025-07-21T07:49:15Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-11-05T13:50:07Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/24-aap2113
ec_funded: 1
external_id:
arxiv:
- '2308.00516'
isi:
- '001434322900006'
intvolume: ' 35'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2308.00516
month: '02'
oa: 1
oa_version: Preprint
page: 196 - 250
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: The Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '17351'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Contractive coupling rates and curvature lower bounds for Markov chains
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20050'
abstract:
- lang: eng
text: We prove upper bounds on the L∞-Wasserstein distance from optimal transport
between strongly log-concave probability densities and log-Lipschitz perturbations.
In the simplest setting, such a bound amounts to a transport-information inequality
involving the L∞-Wasserstein metric and the relative L∞-Fisher information. We
show that this inequality can be sharpened significantly in situations where the
involved densities are anisotropic. Our proof is based on probabilistic techniques
using Langevin dynamics. As an application of these results, we obtain sharp exponential
rates of convergence in Fisher’s infinitesimal model from quantitative genetics,
generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1
to arbitrary dimensions.
acknowledgement: This research was funded in part by the Austrian Science Fund (FWF)
project 10.55776/F65 and the Austrian Academy of Science, DOC fellowship nr. 26293.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kseniia
full_name: Khudiakova, Kseniia
id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
last_name: Khudiakova
orcid: 0000-0002-6246-1465
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave
measures and exponential convergence in Fisher’s infinitesimal model. The Annals
of Applied Probability. 2025;35(3):1913-1940. doi:10.1214/25-aap2162
apa: Khudiakova, K., Maas, J., & Pedrotti, F. (2025). L∞-optimal transport of
anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal
model. The Annals of Applied Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/25-aap2162
chicago: Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport
of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal
Model.” The Annals of Applied Probability. Institute of Mathematical Statistics,
2025. https://doi.org/10.1214/25-aap2162.
ieee: K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic
log-concave measures and exponential convergence in Fisher’s infinitesimal model,”
The Annals of Applied Probability, vol. 35, no. 3. Institute of Mathematical
Statistics, pp. 1913–1940, 2025.
ista: Khudiakova K, Maas J, Pedrotti F. 2025. L∞-optimal transport of anisotropic
log-concave measures and exponential convergence in Fisher’s infinitesimal model.
The Annals of Applied Probability. 35(3), 1913–1940.
mla: Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave
Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” The
Annals of Applied Probability, vol. 35, no. 3, Institute of Mathematical Statistics,
2025, pp. 1913–40, doi:10.1214/25-aap2162.
short: K. Khudiakova, J. Maas, F. Pedrotti, The Annals of Applied Probability 35
(2025) 1913–1940.
corr_author: '1'
date_created: 2025-07-21T08:13:54Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2025-09-30T14:12:48Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/25-aap2162
external_id:
arxiv:
- '2402.04151'
isi:
- '001523520000012'
intvolume: ' 35'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2402.04151
month: '06'
oa: 1
oa_version: Preprint
page: 1913-1940
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8
grant_number: '26293'
name: The impact of deleterious mutations on small populations
publication: The Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '17352'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: L∞-optimal transport of anisotropic log-concave measures and exponential convergence
in Fisher’s infinitesimal model
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 35
year: '2025'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20591'
abstract:
- lang: eng
text: In this paper we derive estimates for the Hessian of the logarithm (log-Hessian)
for solutions to the heat equation. For initial data in the form of log-Lipschitz
perturbation of strongly log-concave measures, the log-Hessian admits an explicit,
uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant
of a transport map pushing forward the standard Gaussian to a measure in this
class. On the other hand, we show that assuming only fast decay of the tails of
the initial datum does not suffice to guarantee uniform log-Hessian upper bounds.
acknowledgement: This research was funded in part by the Austrian Science Fund (FWF)
project 10.55776/F65 and by the European Union’s Horizon 2020 research and innovation
programme under the Marie Sklodowska-Curie grant agreement No 101034413. The authors
thank Professors Jean Dolbeault, Jan Maas, and Nikita Simonov for many useful comments,
and Professors Kazuhiro Ishige, Asuka Takatsu, and Yair Shenfeld for inspiring interactions.
article_number: '71'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps.
Electronic Communications in Probability. 2025;30. doi:10.1214/25-ECP717
apa: Brigati, G., & Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz
transport maps. Electronic Communications in Probability. Institute of
Mathematical Statistics. https://doi.org/10.1214/25-ECP717
chicago: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and
Lipschitz Transport Maps.” Electronic Communications in Probability. Institute
of Mathematical Statistics, 2025. https://doi.org/10.1214/25-ECP717.
ieee: G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport
maps,” Electronic Communications in Probability, vol. 30. Institute of
Mathematical Statistics, 2025.
ista: Brigati G, Pedrotti F. 2025. Heat flow, log-concavity, and Lipschitz transport
maps. Electronic Communications in Probability. 30, 71.
mla: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz
Transport Maps.” Electronic Communications in Probability, vol. 30, 71,
Institute of Mathematical Statistics, 2025, doi:10.1214/25-ECP717.
short: G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025).
corr_author: '1'
date_created: 2025-11-02T23:01:35Z
date_published: 2025-09-25T00:00:00Z
date_updated: 2025-12-01T15:08:54Z
day: '25'
ddc:
- '500'
department:
- _id: JaMa
doi: 10.1214/25-ECP717
ec_funded: 1
external_id:
arxiv:
- '2404.15205'
isi:
- '001611557000018'
file:
- access_level: open_access
checksum: 67858edbd74658fe38955fa1216f2f18
content_type: application/pdf
creator: dernst
date_created: 2025-11-04T07:34:05Z
date_updated: 2025-11-04T07:34:05Z
file_id: '20596'
file_name: 2025_ElectronJourProbab_Brigati.pdf
file_size: 278078
relation: main_file
success: 1
file_date_updated: 2025-11-04T07:34:05Z
has_accepted_license: '1'
intvolume: ' 30'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Electronic Communications in Probability
publication_identifier:
eissn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '17353'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Heat flow, log-concavity, and Lipschitz transport maps
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20569'
abstract:
- lang: eng
text: 'This is the first part of a general description in terms of mass transport
for time-evolving interacting particles systems, at a mesoscopic level. Beyond
kinetic theory, our framework naturally applies in biology, computer vision, and
engineering. The central object of our study is a new discrepancy d between two
probability distributions in position and velocity states, which is reminiscent
of the 2-Wasserstein distance, but of second-order nature. We construct d in two
steps. First, we optimise over transport plans. The cost function is given by
the minimal acceleration between two coupled states on a fixed time horizon T.
Second, we further optimise over the time horizon T > 0. We prove the existence
of optimal transport plans and maps, and study two time-continuous characterisations
of d. One is given in terms of dynamical transport plans. The other one -- in
the spirit of the Benamou--Brenier formula -- is formulated as the minimisation
of an action of the acceleration field, constrained by Vlasov''s equations. Equivalence
of static and dynamical formulations of d holds true. While part of this result
can be derived from recent, parallel developments in optimal control between measures,
we give an original proof relying on two new ingredients: Galilean regularisation
of Vlasov''s equations and a kinetic Monge--Mather shortening principle. Finally,
we establish a first-order differential calculus in the geometry induced by d,
and identify solutions to Vlasov''s equations with curves of measures satisfying
a certain d-absolute continuity condition. One consequence is an explicit formula
for the d-derivative of such curves.'
acknowledgement: "This work was partially inspired by an unpublished note from 2014
by Guillaume Carlier,\r\nJean Dolbeault, and Bruno Nazaret. GB deeply thanks Jean
Dolbeault for proposing\r\nthis problem to him, guiding him into the subject, and
sharing the aforementioned note.\r\nWe are grateful to Karthik Elamvazhuthi for
making us aware of the work [20].\r\nThe work of GB has received funding from the
European Union’s Horizon 2020 research and innovation programme under the Marie
Sklodowska-Curie grant agreement\r\nNo 101034413.\r\nJM and FQ gratefully acknowledge
support from the Austrian Science Fund (FWF)\r\nproject 10.55776/F65."
article_number: '2502.15665'
article_processing_charge: No
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: 'Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part
1: Second-order discrepancies between probability measures. arXiv. doi:10.48550/arXiv.2502.15665'
apa: 'Brigati, G., Maas, J., & Quattrocchi, F. (n.d.). Kinetic Optimal Transport
(OTIKIN) -- Part 1: Second-order discrepancies between probability measures. arXiv.
https://doi.org/10.48550/arXiv.2502.15665'
chicago: 'Brigati, Giovanni, Jan Maas, and Filippo Quattrocchi. “Kinetic Optimal
Transport (OTIKIN) -- Part 1: Second-Order Discrepancies between Probability Measures.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2502.15665.'
ieee: 'G. Brigati, J. Maas, and F. Quattrocchi, “Kinetic Optimal Transport (OTIKIN)
-- Part 1: Second-order discrepancies between probability measures,” arXiv.
.'
ista: 'Brigati G, Maas J, Quattrocchi F. Kinetic Optimal Transport (OTIKIN) -- Part
1: Second-order discrepancies between probability measures. arXiv, 2502.15665.'
mla: 'Brigati, Giovanni, et al. “Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order
Discrepancies between Probability Measures.” ArXiv, 2502.15665, doi:10.48550/arXiv.2502.15665.'
short: G. Brigati, J. Maas, F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:08Z
date_published: 2025-08-10T00:00:00Z
date_updated: 2026-08-07T22:31:03Z
day: '10'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2502.15665
ec_funded: 1
external_id:
arxiv:
- '2502.15665'
keyword:
- optimal transport
- kinetic theory
- second-order discrepancy
- Vlasov equation
- Wasserstein splines.
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.15665
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: 'Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between
probability measures'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
_id: '14451'
abstract:
- lang: eng
text: 'We investigate the potential of Multi-Objective, Deep Reinforcement Learning
for stock and cryptocurrency single-asset trading: in particular, we consider
a Multi-Objective algorithm which generalizes the reward functions and discount
factor (i.e., these components are not specified a priori, but incorporated in
the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT,
XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of
the proposed Multi-Objective algorithm, and provide preliminary statistical evidence
showing increased predictive stability over the corresponding Single-Objective
strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge
over the corresponding Single-Objective strategy when the reward mechanism is
sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss
the generalization properties with respect to the discount factor. The entirety
of our code is provided in open-source format.'
acknowledgement: Open access funding provided by Università degli Studi di Trieste
within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant
No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Constantin
full_name: Disselkamp, Constantin
last_name: Disselkamp
- first_name: Davide
full_name: Scassola, Davide
last_name: Scassola
- first_name: Christopher
full_name: Helf, Christopher
last_name: Helf
citation:
ama: 'Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization:
Improving performance of Deep Reinforcement Learning for applications in single-asset
trading. Neural Computing and Applications. 2024;36(2):617-637. doi:10.1007/s00521-023-09033-7'
apa: 'Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2024). Multi-objective
reward generalization: Improving performance of Deep Reinforcement Learning for
applications in single-asset trading. Neural Computing and Applications.
Springer Nature. https://doi.org/10.1007/s00521-023-09033-7'
chicago: 'Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher
Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement
Learning for Applications in Single-Asset Trading.” Neural Computing and Applications.
Springer Nature, 2024. https://doi.org/10.1007/s00521-023-09033-7.'
ieee: 'F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward
generalization: Improving performance of Deep Reinforcement Learning for applications
in single-asset trading,” Neural Computing and Applications, vol. 36, no.
2. Springer Nature, pp. 617–637, 2024.'
ista: 'Cornalba F, Disselkamp C, Scassola D, Helf C. 2024. Multi-objective reward
generalization: Improving performance of Deep Reinforcement Learning for applications
in single-asset trading. Neural Computing and Applications. 36(2), 617–637.'
mla: 'Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving
Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.”
Neural Computing and Applications, vol. 36, no. 2, Springer Nature, 2024,
pp. 617–37, doi:10.1007/s00521-023-09033-7.'
short: F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications
36 (2024) 617–637.
corr_author: '1'
date_created: 2023-10-22T22:01:16Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2025-04-23T07:39:14Z
day: '01'
ddc:
- '000'
department:
- _id: JuFi
doi: 10.1007/s00521-023-09033-7
ec_funded: 1
external_id:
arxiv:
- '2203.04579'
pmid:
- '38187995'
file:
- access_level: open_access
checksum: 04573d8e74c6119b97c2ca0a984e19a1
content_type: application/pdf
creator: dernst
date_created: 2024-07-16T08:08:54Z
date_updated: 2024-07-16T08:08:54Z
file_id: '17251'
file_name: 2024_NeuralCompApplications_Cornalba.pdf
file_size: 4412285
relation: main_file
success: 1
file_date_updated: 2024-07-16T08:08:54Z
has_accepted_license: '1'
intvolume: ' 36'
issue: '2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 617-637
pmid: 1
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Neural Computing and Applications
publication_identifier:
eissn:
- 1433-3058
issn:
- 0941-0643
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multi-objective reward generalization: Improving performance of Deep Reinforcement
Learning for applications in single-asset trading'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2024'
...
---
_id: '14884'
abstract:
- lang: eng
text: We perform a stochastic homogenization analysis for composite materials exhibiting
a random microstructure. Under the assumptions of stationarity and ergodicity,
we characterize the Gamma-limit of a micromagnetic energy functional defined on
magnetizations taking value in the unit sphere and including both symmetric and
antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic
energy functional with homogeneous coefficients. We provide explicit formulas
for the effective magnetic properties of the composite material in terms of homogenization
correctors. Additionally, the variational analysis of the two exchange energy
terms is performed in the more general setting of functionals defined on manifold-valued
maps with Sobolev regularity, in the case in which the target manifold is a bounded,
orientable smooth surface with tubular neighborhood of uniform thickness. Eventually,
we present an explicit characterization of minimizers of the effective exchange
in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s
predictions on the emergence of helical structures in composite ferromagnetic
materials with stochastic microstructure.
acknowledgement: All authors acknowledge support of the Austrian Science Fund (FWF)
through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally
been supported by the FWF through grants V662, Y1292, and P35359, as well as from
OeAD through the WTZ grant CZ09/2023.
article_number: '30'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elisa
full_name: Davoli, Elisa
last_name: Davoli
- first_name: Lorenza
full_name: D’Elia, Lorenza
last_name: D’Elia
- first_name: Jonas
full_name: Ingmanns, Jonas
id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
last_name: Ingmanns
citation:
ama: Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions. Journal of Nonlinear Science.
2024;34(2). doi:10.1007/s00332-023-10005-3
apa: Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization
of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear
Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3
chicago: Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization
of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of
Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3.
ieee: E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science,
vol. 34, no. 2. Springer Nature, 2024.
ista: Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2),
30.
mla: Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies
and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol.
34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3.
short: E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).
date_created: 2024-01-28T23:01:42Z
date_published: 2024-01-23T00:00:00Z
date_updated: 2025-09-04T11:54:01Z
day: '23'
department:
- _id: JuFi
doi: 10.1007/s00332-023-10005-3
external_id:
arxiv:
- '2306.05151'
isi:
- '001147480200001'
intvolume: ' 34'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.05151
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Nonlinear Science
publication_identifier:
eissn:
- 1432-1467
issn:
- 0938-8974
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stochastic homogenization of micromagnetic energies and emergence of magnetic
skyrmions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 34
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14934'
abstract:
- lang: eng
text: "We study random perturbations of a Riemannian manifold (M, g) by means of
so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the
given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the
conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular
case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated
Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric
and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion,
spectral bound, or spectral gap change under the influence of the noise. And if
so, is\r\nit possible to quantify these dependencies in terms of key parameters
of the noise? Another\r\ngoal is to define and analyze in detail the Fractional
Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent
interest."
acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for
valuable discussions on this project. They are also grateful to Nathanaël Berestycki,
and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24],
and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous
version of the proof of Proposition 3.10. The authors feel very much indebted to
an anonymous reviewer for his/her careful reading and the many valuable suggestions
that have significantly contributed to the improvement of the paper. L.D.S. gratefully
acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC
1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65
at Institute of Science and Technology Austria. This research was funded in whole
or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open
access, the authors have applied a CC BY public copyright licence to any Author
Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff
Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian
geometry. Potential Analysis. 2024;61:501-553. doi:10.1007/s11118-023-10118-0
apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour
in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0
chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery
Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature,
2024. https://doi.org/10.1007/s11118-023-10118-0.
ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random
Riemannian geometry,” Potential Analysis, vol. 61. Springer Nature, pp.
501–553, 2024.
ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian
geometry. Potential Analysis. 61, 501–553.
mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.”
Potential Analysis, vol. 61, Springer Nature, 2024, pp. 501–53, doi:10.1007/s11118-023-10118-0.
short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis 61 (2024) 501–553.
date_created: 2024-02-04T23:00:54Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T11:57:14Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-023-10118-0
external_id:
arxiv:
- '2012.06796'
isi:
- '001151118800001'
file:
- access_level: open_access
checksum: 33c688bdf296c3d8f8bbd96c7dd26037
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:13:34Z
date_updated: 2025-01-09T08:13:34Z
file_id: '18789'
file_name: 2024_PotentialAnalysis_DelloSchiavo.pdf
file_size: 1294993
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:13:34Z
has_accepted_license: '1'
intvolume: ' 61'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 501-553
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A discovery tour in random Riemannian geometry
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 61
year: '2024'
...
---
_id: '15317'
abstract:
- lang: eng
text: 'We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes
on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random
walks on Ω dual to SEP/SIP we establish: a functional-CLT-type convergence to
the Brownian motion on Ω with either Neumann (slow boundary), Dirichlet (fast
boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum
convergence of the corresponding harmonic profiles. As a consequence, we rigorously
derive the hydrodynamic and hydrostatic limits for SEP/SIP on Ω, and analyze their
stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP
concern finite-dimensional distribution convergence only, as our duality techniques
do not require to establish tightness for the fields associated to the particle
systems.'
acknowledgement: "The first author gratefully acknowledges funding by the Austrian
Science Fund (FWF) grant F65, by the European Research Council (ERC, grant agreement
No 716117, awarded to Prof. Dr. Jan Maas). He also gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) grant ESPRIT 208.\r\nThe
second author gratefully acknowledges funding by the Hausdorff Center for Mathematics
at the University of Bonn. Part of this work was completed while this author was
a member of the Institute of Science and Technology Austria. He gratefully acknowledges
funding of his position at that time by the Austrian Science Fund (FWF) grants F65
and W1245.\r\nThe third author gratefully acknowledges funding by the Lise Meitner
fellowship, Austrian Science Fund (FWF): M3211. Part of this work was completed
while funded by the European Union’s Horizon 2020 research and innovation programme
under the Marie-Skłodowska-Curie grant agreement No. 754411."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Dello Schiavo L, Portinale L, Sau F. Scaling limits of random walks, harmonic
profiles, and stationary nonequilibrium states in Lipschitz domains. Annals
of Applied Probability. 2024;34(2):1789-1845. doi:10.1214/23-AAP2007
apa: Dello Schiavo, L., Portinale, L., & Sau, F. (2024). Scaling limits of random
walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains.
Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2007
chicago: Dello Schiavo, Lorenzo, Lorenzo Portinale, and Federico Sau. “Scaling Limits
of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz
Domains.” Annals of Applied Probability. Institute of Mathematical Statistics,
2024. https://doi.org/10.1214/23-AAP2007.
ieee: L. Dello Schiavo, L. Portinale, and F. Sau, “Scaling limits of random walks,
harmonic profiles, and stationary nonequilibrium states in Lipschitz domains,”
Annals of Applied Probability, vol. 34, no. 2. Institute of Mathematical
Statistics, pp. 1789–1845, 2024.
ista: Dello Schiavo L, Portinale L, Sau F. 2024. Scaling limits of random walks,
harmonic profiles, and stationary nonequilibrium states in Lipschitz domains.
Annals of Applied Probability. 34(2), 1789–1845.
mla: Dello Schiavo, Lorenzo, et al. “Scaling Limits of Random Walks, Harmonic Profiles,
and Stationary Nonequilibrium States in Lipschitz Domains.” Annals of Applied
Probability, vol. 34, no. 2, Institute of Mathematical Statistics, 2024, pp.
1789–845, doi:10.1214/23-AAP2007.
short: L. Dello Schiavo, L. Portinale, F. Sau, Annals of Applied Probability 34
(2024) 1789–1845.
corr_author: '1'
date_created: 2024-04-14T22:01:02Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-09-04T13:36:00Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/23-AAP2007
ec_funded: 1
external_id:
arxiv:
- '2112.14196'
isi:
- '001198623200016'
intvolume: ' 34'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2112.14196
month: '04'
oa: 1
oa_version: Preprint
page: 1789-1845
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 3490b268-11ca-11ed-8bc3-e0ad03f48839
grant_number: M03211
name: Reaching consensus in heterogeneous random opinion dynamics
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1245
name: Dissipation and dispersion in nonlinear partial differential equations
publication: Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium
states in Lipschitz domains
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 34
year: '2024'
...
---
_id: '17143'
abstract:
- lang: eng
text: "This paper deals with local criteria for the convergence to a global minimiser
for gradient flow trajectories and their discretisations. To obtain quantitative
estimates on the speed of convergence, we consider variations on the classical
Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions
are given in terms of the initial data, without any reference to an equilibrium
point. The main results are convergence statements for gradient flow curves and
proximal point sequences to a global minimiser, together with sharp quantitative
estimates on the speed of convergence. These convergence results apply in the
general setting of lower semicontinuous functionals on complete metric spaces,
generalising recent results for smooth functionals on Rn. While the non-smooth
setting covers very general spaces, it is also useful for (non)-smooth functionals
on Rn.\r\n."
acknowledgement: The authors gratefully acknowledges support by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No. 716117). This research was funded in part by the Austrian Science
Fund (FWF) project 10.55776/ESP208. This research was funded in part by the Austrian
Science Fund (FWF) project 10.55776/F65
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence
of gradient flows and proximal point sequences in metric spaces. Transactions
of the American Mathematical Society. 2024;377(6):3779-3804. doi:10.1090/tran/9156
apa: Dello Schiavo, L., Maas, J., & Pedrotti, F. (2024). Local conditions for
global convergence of gradient flows and proximal point sequences in metric spaces.
Transactions of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/tran/9156
chicago: Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions
for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric
Spaces.” Transactions of the American Mathematical Society. American Mathematical
Society, 2024. https://doi.org/10.1090/tran/9156.
ieee: L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence
of gradient flows and proximal point sequences in metric spaces,” Transactions
of the American Mathematical Society, vol. 377, no. 6. American Mathematical
Society, pp. 3779–3804, 2024.
ista: Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence
of gradient flows and proximal point sequences in metric spaces. Transactions
of the American Mathematical Society. 377(6), 3779–3804.
mla: Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of
Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions
of the American Mathematical Society, vol. 377, no. 6, American Mathematical
Society, 2024, pp. 3779–804, doi:10.1090/tran/9156.
short: L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical
Society 377 (2024) 3779–3804.
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-04-07T13:00:02Z
day: '01'
department:
- _id: JaMa
doi: 10.1090/tran/9156
ec_funded: 1
external_id:
arxiv:
- '2304.05239'
isi:
- '001203273300001'
intvolume: ' 377'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2304.05239
month: '06'
oa: 1
oa_version: Preprint
page: 3779-3804
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Transactions of the American Mathematical Society
publication_identifier:
eissn:
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issn:
- 0002-9947
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local conditions for global convergence of gradient flows and proximal point
sequences in metric spaces
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 377
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18490'
abstract:
- lang: eng
text: 'For large classes of even-dimensional Riemannian manifolds (Formula presented.),
we construct and analyze conformally invariant random fields. These centered Gaussian
fields (Formula presented.), called co-polyharmonic Gaussian fields, are characterized
by their covariance kernels k which exhibit a precise logarithmic divergence:
(Formula presented.). They share a fundamental quasi-invariance property under
conformal transformations. In terms of the co-polyharmonic Gaussian field (Formula
presented.), we define the Liouville Quantum Gravity measure, a random measure
on (Formula presented.), heuristically given as (Formula presented.) and rigorously
obtained as almost sure weak limit of the right-hand side with (Formula presented.)
replaced by suitable regular approximations (Formula presented.). In terms on
the Liouville Quantum Gravity measure, we define the Liouville Brownian motion
on (Formula presented.) and the random GJMS operators. Finally, we present an
approach to a conformal field theory in arbitrary even dimension with an ansatz
based on Branson''s (Formula presented.) -curvature: we give a rigorous meaning
to the Polyakov–Liouville measure (Formula presented.) and we derive the corresponding
conformal anomaly. The set of admissible manifolds is conformally invariant. It
includes all compact 2-dimensional Riemannian manifolds, all compact non-negatively
curved Einstein manifolds of even dimension, and large classes of compact hyperbolic
manifolds of even dimension. However, not every compact even-dimensional Riemannian
manifold is admissible. Our results concerning the logarithmic divergence of the
kernel (Formula presented.) rely on new sharp estimates for heat kernels and higher
order Green kernels on arbitrary closed manifolds. '
acknowledgement: The authors are grateful to Masha Gordina for helpful references,
and to Nathanaël Berestycki, Baptiste Cerclé, and Ewain Gwynne for valuable comments
on the first circulated version of this paper. They also would like to thank Sebastian
Andres, Peter Friz, and Yizheng Yuan for pointing out an erroneous formulation in
the previous version of Theorem 5.7. Moreover, KTS would liketo express his thanks
to Sebastian Andres, Matthias Erbar, Martin Huesmann, and Jan Mass for stimulating
discussions on previous attempts to this project. LDS gratefully acknowledges financial
support from the European Research Council (grant agreement No 716117, awarded to
J. Maas), from the Austrian Science Fund (FWF) project 10.55776/ESP208, and from
the Austrian Science Fund (FWF) project 10.55776/F65.RH, EK, and KTS gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the project “Random
Riemannian Geometry” within the SPP 2265 “Random Geomet-ric Systems,” through the
Hausdorff Center for Mathematics (project ID 390685813), and through project B03
within the CRC 1060 (project ID 211504053). RH and KTS also gratefully acknowledge
financial support from the European Research Council through the ERC AdG “RicciBounds”(grant
agreement 694405).Data sharing not applicable to this article as no datasets were
generated or analyzed during the current study. Open access funding enabled and
organized by Projekt DEAL.
article_number: e70003
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Ronan
full_name: Herry, Ronan
last_name: Herry
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Conformally invariant random
fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian
manifolds of even dimension. Journal of the London Mathematical Society.
2024;110(5). doi:10.1112/jlms.70003
apa: Dello Schiavo, L., Herry, R., Kopfer, E., & Sturm, K. T. (2024). Conformally
invariant random fields, Liouville quantum gravity measures, and random Paneitz
operators on Riemannian manifolds of even dimension. Journal of the London
Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.70003
chicago: Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm.
“Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and
Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” Journal
of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.70003.
ieee: L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Conformally invariant
random fields, Liouville quantum gravity measures, and random Paneitz operators
on Riemannian manifolds of even dimension,” Journal of the London Mathematical
Society, vol. 110, no. 5. London Mathematical Society, 2024.
ista: Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2024. Conformally invariant
random fields, Liouville quantum gravity measures, and random Paneitz operators
on Riemannian manifolds of even dimension. Journal of the London Mathematical
Society. 110(5), e70003.
mla: Dello Schiavo, Lorenzo, et al. “Conformally Invariant Random Fields, Liouville
Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds
of Even Dimension.” Journal of the London Mathematical Society, vol. 110,
no. 5, e70003, London Mathematical Society, 2024, doi:10.1112/jlms.70003.
short: L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Journal of the London
Mathematical Society 110 (2024).
date_created: 2024-11-03T23:01:44Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-08T14:29:45Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1112/jlms.70003
ec_funded: 1
external_id:
isi:
- '001351918100029'
file:
- access_level: open_access
checksum: 143816823b5f43bd3748da8e3e91cef5
content_type: application/pdf
creator: dernst
date_created: 2024-11-04T08:54:26Z
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oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Conformally invariant random fields, Liouville quantum gravity measures, and
random Paneitz operators on Riemannian manifolds of even dimension
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 110
year: '2024'
...
---
OA_place: publisher
OA_type: gold
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abstract:
- lang: eng
text: 'Score-based generative models (SGMs) are powerful tools to sample from complex
data distributions. Their underlying idea is to (i) run a forward process for
time T1 by adding noise to the data, (ii) estimate its score function, and (iii)
use such estimate to run a reverse process. As the reverse process is initialized
with the stationary distribution of the forward one, the existing analysis paradigm
requires T1→∞. This is however problematic: from a theoretical viewpoint, for
a given precision of the score approximation, the convergence guarantee fails
as T1 diverges; from a practical viewpoint, a large T1 increases computational
costs and leads to error propagation. This paper addresses the issue by considering
a version of the popular predictor-corrector scheme: after running the forward
process, we first estimate the final distribution via an inexact Langevin dynamics
and then revert the process. Our key technical contribution is to provide convergence
guarantees which require to run the forward process only for a fixed finite time
T1. Our bounds exhibit a mild logarithmic dependence on the input dimension and
the subgaussian norm of the target distribution, have minimal assumptions on the
data, and require only to control the L2 loss on the score approximation, which
is the quantity minimized in practice.'
acknowledgement: "Francesco Pedrotti and Jan Maas acknowledge support by the Austrian
Science Fund (FWF) project 10.55776/F65. Marco Mondelli acknowledges support by
the 2019 Lopez-Loreta prize.\r\n"
alternative_title:
- TMLR
article_processing_charge: No
arxiv: 1
author:
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion
models via prediction-correction. In: Transactions on Machine Learning Research.
; 2024.'
apa: Pedrotti, F., Maas, J., & Mondelli, M. (2024). Improved convergence of
score-based diffusion models via prediction-correction. In Transactions on
Machine Learning Research.
chicago: Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence
of Score-Based Diffusion Models via Prediction-Correction.” In Transactions
on Machine Learning Research, 2024.
ieee: F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based
diffusion models via prediction-correction,” in Transactions on Machine Learning
Research, 2024.
ista: Pedrotti F, Maas J, Mondelli M. 2024. Improved convergence of score-based
diffusion models via prediction-correction. Transactions on Machine Learning Research.
, TMLR, .
mla: Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion
Models via Prediction-Correction.” Transactions on Machine Learning Research,
2024.
short: F. Pedrotti, J. Maas, M. Mondelli, in:, Transactions on Machine Learning
Research, 2024.
corr_author: '1'
date_created: 2025-01-27T12:18:05Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-04-15T08:31:35Z
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ddc:
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- _id: MaMo
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- '2305.14164'
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publication_status: published
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status: public
scopus_import: '1'
status: public
title: Improved convergence of score-based diffusion models via prediction-correction
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '17282'
abstract:
- lang: eng
text: Let X be a vector field and Y be a co-vector field on a smooth manifold M.
Does there exist a smooth Riemannian metric gαβ on M such that Yβ=gαβXα ?
The main result of this note gives necessary and sufficient conditions for this
to be true. As an application of this result we show that a finite-dimensional
ergodic Lindblad equation admits a gradient flow structure for the von Neumann
relative entropy if and only if the condition of BKM-detailed balance holds.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).J. M. gratefully acknowledges support by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB
F65. We thank the anonymous referee for valuable comments on the paper.
article_number: '153'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Brooks M, Maas J. Characterisation of gradient flows for a given functional.
Calculus of Variations and Partial Differential Equations. 2024;63(6).
doi:10.1007/s00526-024-02755-z
apa: Brooks, M., & Maas, J. (2024). Characterisation of gradient flows for a
given functional. Calculus of Variations and Partial Differential Equations.
Springer Nature. https://doi.org/10.1007/s00526-024-02755-z
chicago: Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a
given Functional.” Calculus of Variations and Partial Differential Equations.
Springer Nature, 2024. https://doi.org/10.1007/s00526-024-02755-z.
ieee: M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,”
Calculus of Variations and Partial Differential Equations, vol. 63, no.
6. Springer Nature, 2024.
ista: Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional.
Calculus of Variations and Partial Differential Equations. 63(6), 153.
mla: Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given
Functional.” Calculus of Variations and Partial Differential Equations,
vol. 63, no. 6, 153, Springer Nature, 2024, doi:10.1007/s00526-024-02755-z.
short: M. Brooks, J. Maas, Calculus of Variations and Partial Differential Equations
63 (2024).
corr_author: '1'
date_created: 2024-07-21T22:01:01Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:24:51Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-024-02755-z
ec_funded: 1
external_id:
arxiv:
- '2209.11149'
isi:
- '001258097800003'
pmid:
- '38947856'
file:
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checksum: a0cf0e0ba2157aabb287cb597be17dac
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project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
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grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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status: public
title: Characterisation of gradient flows for a given functional
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year: '2024'
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abstract:
- lang: eng
text: "This thesis deals with the study of stochastic processes and their ergodicity
properties. The\r\nvariety of problems encountered calls for a set of different
approaches, ranging from classical to\r\nmodern ones: a special place is held
by probabilistic methods based on couplings, by functional\r\ninequalities, and
by the theory of gradient flows in the space of measures.\r\n\r\nThe material
is organized as follows. Chapter 1 contains the introduction to this thesis, starting\r\nwith
a general presentation of some of the relevant topics. Section 1.1 is dedicated
to the\r\ntheory of gradient flows in metric spaces, and introduces the first
contribution of this thesis\r\n[DSMP24], which is presented in detail in Chapter
2. Section 1.2 moves to the topic of\r\ncurvature of Markov chains, concluding
with a brief description of our second contribution\r\n[Ped23], which is included
in Chapter 3. Section 1.3 discusses applications of stochastic\r\nprocesses to
the theory of sampling, in particular the recent framework of score-based diffusion\r\nmodels,
and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses\r\nsome
related problems, concerning the regularization properties of the heat flow. It
serves\r\nas a motivation for the work [BP24], which we report in Chapter 5. Finally,
Section 1.5\r\ndiscusses the last contribution of this thesis, which can be found
in Chapter 6. It deals with\r\nthe convergence to equilibrium of a particular
stochastic model from quantitative genetics:\r\nthis is established via some functional
inequalities, which we prove with probabilistic arguments\r\nbased on couplings.\r\n"
alternative_title:
- ISTA Thesis
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author:
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Pedrotti F. Functional inequalities and convergence of stochastic processes.
2024. doi:10.15479/at:ista:17336
apa: Pedrotti, F. (2024). Functional inequalities and convergence of stochastic
processes. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17336
chicago: Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic
Processes.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17336.
ieee: F. Pedrotti, “Functional inequalities and convergence of stochastic processes,”
Institute of Science and Technology Austria, 2024.
ista: Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes.
Institute of Science and Technology Austria.
mla: Pedrotti, Francesco. Functional Inequalities and Convergence of Stochastic
Processes. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17336.
short: F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes,
Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-07-29T09:14:14Z
date_published: 2024-07-31T00:00:00Z
date_updated: 2026-04-07T13:00:03Z
day: '31'
ddc:
- '500'
- '510'
- '515'
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/at:ista:17336
ec_funded: 1
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project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
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- 2663-337X
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publisher: Institute of Science and Technology Austria
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supervisor:
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full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Functional inequalities and convergence of stochastic processes
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