---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21018'
abstract:
- lang: eng
text: In this paper, we review recent results on stability and instability in logarithmic
Sobolev inequalities, with a particular emphasis on strong norms. We consider
several versions of these inequalities on the Euclidean space, for the Lebesgue
and the Gaussian measures, and discuss their differences in terms of moments and
stability. We give new and direct proofs, as well as examples and discuss the
stability of a logarithmic uncertainty principle. Although we do not cover all
aspects of the topic, we hope to contribute to establishing the state of the art.
acknowledgement: This work has been supported by the Project Conviviality (ANR-23-CE40–0003)
of the French National Research Agency. G.B. has received funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
grant agreement No 101034413. The authors thank a referee for a careful reading
and suggestions which result in a significant improvement of the manuscript. Open
access funding provided by Institute of Science and Technology (IST Austria). The
work of GB has received funding from the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.
This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the
French National Research Agency.
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Jean
full_name: Dolbeault, Jean
last_name: Dolbeault
- first_name: Nikita
full_name: Simonov, Nikita
last_name: Simonov
citation:
ama: 'Brigati G, Dolbeault J, Simonov N. Logarithmic Sobolev Inequalities: A review
on stability and instability results. La Matematica. 2026;5. doi:10.1007/s44007-025-00180-y'
apa: 'Brigati, G., Dolbeault, J., & Simonov, N. (2026). Logarithmic Sobolev
Inequalities: A review on stability and instability results. La Matematica.
Springer Nature. https://doi.org/10.1007/s44007-025-00180-y'
chicago: 'Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. “Logarithmic Sobolev
Inequalities: A Review on Stability and Instability Results.” La Matematica.
Springer Nature, 2026. https://doi.org/10.1007/s44007-025-00180-y.'
ieee: 'G. Brigati, J. Dolbeault, and N. Simonov, “Logarithmic Sobolev Inequalities:
A review on stability and instability results,” La Matematica, vol. 5.
Springer Nature, 2026.'
ista: 'Brigati G, Dolbeault J, Simonov N. 2026. Logarithmic Sobolev Inequalities:
A review on stability and instability results. La Matematica. 5, 5.'
mla: 'Brigati, Giovanni, et al. “Logarithmic Sobolev Inequalities: A Review on Stability
and Instability Results.” La Matematica, vol. 5, 5, Springer Nature, 2026,
doi:10.1007/s44007-025-00180-y.'
short: G. Brigati, J. Dolbeault, N. Simonov, La Matematica 5 (2026).
corr_author: '1'
date_created: 2026-01-20T10:14:55Z
date_published: 2026-01-08T00:00:00Z
date_updated: 2026-01-21T07:48:28Z
day: '08'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s44007-025-00180-y
ec_funded: 1
external_id:
arxiv:
- '2504.08658'
file:
- access_level: open_access
checksum: 0702d8397f216555b1d5286e5d77f09c
content_type: application/pdf
creator: dernst
date_created: 2026-01-21T07:45:03Z
date_updated: 2026-01-21T07:45:03Z
file_id: '21025'
file_name: 2026_LaMatematica_Brigati.pdf
file_size: 4992025
relation: main_file
success: 1
file_date_updated: 2026-01-21T07:45:03Z
has_accepted_license: '1'
intvolume: ' 5'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: La Matematica
publication_identifier:
issn:
- 2730-9657
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Logarithmic Sobolev Inequalities: A review on stability and instability results'
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: 5
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '21132'
abstract:
- lang: eng
text: We unify the variational hypocoercivity framework established by D. Albritton,
S. Armstrong, J.-C. Mourrat, and M. Novack [2], with the notion of second-order
lifts of reversible diffusion processes, recently introduced by A. Eberle and
the second author [30]. We give an abstract, yet fully constructive, presentation
of the theory, so that it can be applied to a large class of linear kinetic equations.
As this hypocoercivity technique does not twist the reference norm, we can recover
accurate and sharp convergence rates in various models. Among those, adaptive
Langevin dynamics (ALD) is discussed in full detail and we show that for near-quadratic
potentials, with suitable choices of parameters, it is a near-optimal second-order
lift of the overdamped Langevin dynamics. As a further consequence, we observe
that the Generalised Langevin Equation (GLE) is also a second-order lift, as the
standard (kinetic) Langevin dynamics are, of the overdamped Langevin dynamics.
Then, convergence of (GLE) cannot exceed ballistic speed, i.e. the square root
of the rate of the overdamped regime. We illustrate this phenomenon with explicit
computations in a benchmark Gaussian case.
acknowledgement: "We would like to thank Andreas Eberle and Gabriel Stoltz for many
helpful discussions. GB\r\nhas received funding from the European Union Horizon
2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement
No 101034413. FL wurde gefördert durch die Deutsche Forschungsgemeinschaft (DFG)
im Rahmen der Exzellenzstrategie des Bundes und der Länder – GZ2047/1, Projekt-ID
390685813. LW is supported by the National Science Foundation via grant DMS-2407166.
He is also indebted to the Mathematical Sciences department at Carnegie Mellon University
for partly supporting his visit to Europe in July 2024. Part of this work was completed
when GB and LW were visiting the Institute for Applied Mathematics in Bonn. GB and
LW would like to thank IAM for their hospitality."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Francis
full_name: Lörler, Francis
last_name: Lörler
- first_name: Lihan
full_name: Wang, Lihan
last_name: Wang
citation:
ama: Brigati G, Lörler F, Wang L. Hypocoercivity meets lifts. Kinetic and Related
Models. 2026;20:34-55. doi:10.3934/krm.2025020
apa: Brigati, G., Lörler, F., & Wang, L. (2026). Hypocoercivity meets lifts.
Kinetic and Related Models. American Institute of Mathematical Sciences.
https://doi.org/10.3934/krm.2025020
chicago: Brigati, Giovanni, Francis Lörler, and Lihan Wang. “Hypocoercivity Meets
Lifts.” Kinetic and Related Models. American Institute of Mathematical
Sciences, 2026. https://doi.org/10.3934/krm.2025020.
ieee: G. Brigati, F. Lörler, and L. Wang, “Hypocoercivity meets lifts,” Kinetic
and Related Models, vol. 20. American Institute of Mathematical Sciences,
pp. 34–55, 2026.
ista: Brigati G, Lörler F, Wang L. 2026. Hypocoercivity meets lifts. Kinetic and
Related Models. 20, 34–55.
mla: Brigati, Giovanni, et al. “Hypocoercivity Meets Lifts.” Kinetic and Related
Models, vol. 20, American Institute of Mathematical Sciences, 2026, pp. 34–55,
doi:10.3934/krm.2025020.
short: G. Brigati, F. Lörler, L. Wang, Kinetic and Related Models 20 (2026) 34–55.
date_created: 2026-02-01T23:01:43Z
date_published: 2026-02-01T00:00:00Z
date_updated: 2026-02-16T10:02:47Z
day: '01'
department:
- _id: JaMa
doi: 10.3934/krm.2025020
ec_funded: 1
external_id:
arxiv:
- '2412.10890'
intvolume: ' 20'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2412.10890
month: '02'
oa: 1
oa_version: Preprint
page: 34-55
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Kinetic and Related Models
publication_identifier:
eissn:
- 1937-5077
issn:
- 1937-5093
publication_status: epub_ahead
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hypocoercivity meets lifts
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '21504'
abstract:
- lang: eng
text: Selecting an appropriate divergence measure is a critical aspect of machine
learning, as it directly impacts model performance. Among the most widely used,
we find the Kullback–Leibler (KL) divergence, originally introduced in kinetic
theory as a measure of relative entropy between probability distributions. Just
as in machine learning, the ability to quantify the proximity of probability distributions
plays a central role in kinetic theory. In this paper, we present a comparative
review of divergence measures rooted in kinetic theory, highlighting their theoretical
foundations and exploring their potential applications in machine learning and
artificial intelligence.
acknowledgement: "This work has been written within the activities of GNCS and GNFM
groups of INdAM (Italian\r\nNational Institute of High Mathematics). G.B. has been
funded by the European Union’s Horizon 2020 research and innovation programme under
the Marie Sklodowska-Curie grant agreement No 101034413. P.G. has been funded by
the European Union - NextGenerationEU, in the framework of the GRINSGrowing Resilient,
INclusive and Sustainable (GRINS PE00000018)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gennaro
full_name: Auricchio, Gennaro
last_name: Auricchio
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Paolo
full_name: Giudici, Paolo
last_name: Giudici
- first_name: Giuseppe
full_name: Toscani, Giuseppe
last_name: Toscani
citation:
ama: 'Auricchio G, Brigati G, Giudici P, Toscani G. From kinetic theory to AI: A
rediscovery of high-dimensional divergences and their properties. Mathematical
Models and Methods in Applied Sciences. 2026. doi:10.1142/S0218202526410010'
apa: 'Auricchio, G., Brigati, G., Giudici, P., & Toscani, G. (2026). From kinetic
theory to AI: A rediscovery of high-dimensional divergences and their properties.
Mathematical Models and Methods in Applied Sciences. World Scientific Publishing.
https://doi.org/10.1142/S0218202526410010'
chicago: 'Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani.
“From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and
Their Properties.” Mathematical Models and Methods in Applied Sciences.
World Scientific Publishing, 2026. https://doi.org/10.1142/S0218202526410010.'
ieee: 'G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “From kinetic theory
to AI: A rediscovery of high-dimensional divergences and their properties,” Mathematical
Models and Methods in Applied Sciences. World Scientific Publishing, 2026.'
ista: 'Auricchio G, Brigati G, Giudici P, Toscani G. 2026. From kinetic theory to
AI: A rediscovery of high-dimensional divergences and their properties. Mathematical
Models and Methods in Applied Sciences.'
mla: 'Auricchio, Gennaro, et al. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional
Divergences and Their Properties.” Mathematical Models and Methods in Applied
Sciences, World Scientific Publishing, 2026, doi:10.1142/S0218202526410010.'
short: G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and
Methods in Applied Sciences (2026).
date_created: 2026-03-29T22:07:08Z
date_published: 2026-03-14T00:00:00Z
date_updated: 2026-03-30T06:56:35Z
day: '14'
department:
- _id: JaMa
doi: 10.1142/S0218202526410010
ec_funded: 1
external_id:
arxiv:
- '2507.11387'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2507.11387
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'From kinetic theory to AI: A rediscovery of high-dimensional divergences and
their properties'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
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'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-025-03193-1
external_id:
arxiv:
- '2403.07803'
file:
- access_level: open_access
checksum: 635370d64abaf444f50f5cca60bba1be
content_type: application/pdf
creator: dernst
date_created: 2026-01-05T12:36:39Z
date_updated: 2026-01-05T12:36:39Z
file_id: '20945'
file_name: 2026_CalculusVariations_Quattrocchi.pdf
file_size: 958382
relation: main_file
success: 1
file_date_updated: 2026-01-05T12:36:39Z
has_accepted_license: '1'
intvolume: ' 65'
issue: '1'
language:
- iso: eng
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
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '20571'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Variational structures for the Fokker-Planck equation with general Dirichlet
boundary conditions
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 65
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: 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'
...
---
OA_place: repository
OA_type: green
_id: '20155'
abstract:
- lang: eng
text: We study time averages for the norm of solutions to kinetic Fokker–Planck
equations associated with general Hamiltonians. We provide fully explicit and
constructive decay estimates for systems subject to a confining potential, allowing
fat-tail, subexponential and (super-)exponential local equilibria, which also
include the classic Maxwellian case. The key step in our estimates is a modified
Poincaré inequality, obtained via a Lions–Poincaré inequality and an averaging
lemma.
acknowledgement: The first author was funded by the European Union's Horizon 2020
research andinnovation program under the Marie Sklodowska-Curie grant agreements
754362 and 101034413,and partially by Project EFI (ANR-17-CE40-0030) of the French
National Research Agency (ANR).The work of the second author was partially funded
by the European Research Council (ERC) underthe European Union's Horizon 2020 research
and innovation programme (grant agreement 810367),and by the Agence Nationale de
la Recherche under grants ANR-19-CE40-0010 (QuAMProcs) andANR-21-CE40-0006 (SINEQ).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Gabriel
full_name: Stoltz, Gabriel
last_name: Stoltz
citation:
ama: Brigati G, Stoltz G. How to construct explicit decay rates for kinetic Fokker–Planck
equations? SIAM Journal on Mathematical Analysis. 2025;57(4):3587-3622.
doi:10.1137/24M1700351
apa: Brigati, G., & Stoltz, G. (2025). How to construct explicit decay rates
for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis.
Society for Industrial and Applied Mathematics. https://doi.org/10.1137/24M1700351
chicago: Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay
Rates for Kinetic Fokker–Planck Equations?” SIAM Journal on Mathematical Analysis.
Society for Industrial and Applied Mathematics, 2025. https://doi.org/10.1137/24M1700351.
ieee: G. Brigati and G. Stoltz, “How to construct explicit decay rates for kinetic
Fokker–Planck equations?,” SIAM Journal on Mathematical Analysis, vol.
57, no. 4. Society for Industrial and Applied Mathematics, pp. 3587–3622, 2025.
ista: Brigati G, Stoltz G. 2025. How to construct explicit decay rates for kinetic
Fokker–Planck equations? SIAM Journal on Mathematical Analysis. 57(4), 3587–3622.
mla: Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay Rates
for Kinetic Fokker–Planck Equations?” SIAM Journal on Mathematical Analysis,
vol. 57, no. 4, Society for Industrial and Applied Mathematics, 2025, pp. 3587–622,
doi:10.1137/24M1700351.
short: G. Brigati, G. Stoltz, SIAM Journal on Mathematical Analysis 57 (2025) 3587–3622.
corr_author: '1'
date_created: 2025-08-10T22:01:29Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-11-05T13:51:40Z
day: '01'
department:
- _id: JaMa
doi: 10.1137/24M1700351
ec_funded: 1
external_id:
arxiv:
- '2302.14506'
isi:
- '001550830900006'
intvolume: ' 57'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2302.14506
month: '08'
oa: 1
oa_version: Preprint
page: 3587-3622
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to construct explicit decay rates for kinetic Fokker–Planck equations?
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
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: 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. 2025;64. doi:10.1007/s11118-025-10251-y
apa: Keller, M., Lenz, D., Schmidt, M., Schwarz, M., & Wirth, M. (2025). 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, 2025.
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. Springer Nature, 2025.
ista: Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2025. Boundary representations
of intermediate forms between a regular Dirichlet form and its active main part.
Potential Analysis. 64, 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, 6, Springer Nature, 2025, doi:10.1007/s11118-025-10251-y.
short: M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis
64 (2025).
date_created: 2025-12-14T23:02:03Z
date_published: 2025-12-03T00:00:00Z
date_updated: 2025-12-15T13:11:24Z
day: '03'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-025-10251-y
ec_funded: 1
external_id:
arxiv:
- '2301.01035'
has_accepted_license: '1'
intvolume: ' 64'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s11118-025-10251-y
month: '12'
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: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
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)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '19565'
abstract:
- lang: eng
text: 'Measuring distances in a multidimensional setting is a challenging problem,
which appears in many fields of science and engineering. In this paper, to measure
the distance between two multivariate distributions, we introduce a new measure
of discrepancy which is scale invariant and which, in the case of two independent
copies of the same distribution, and after normalization, coincides with the scaling
invariant multidimensional version of the Gini index recently proposed in [P.
Giudici, E. Raffinetti and G. Toscani, Measuring multidimensional inequality:
A new proposal based on the Fourier transform, preprint (2024), arXiv:2401.14012
]. A byproduct of the analysis is an easy-to-handle discrepancy metric, obtained
by application of the theory to a pair of Gaussian multidimensional densities.
The obtained metric does improve the standard metrics, based on the mean squared
error, as it is scale invariant. The importance of this theoretical finding is
illustrated by means of a real problem that concerns measuring the importance
of Environmental, Social and Governance factors for the growth of small and medium
enterprises. '
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gennaro
full_name: Auricchio, Gennaro
last_name: Auricchio
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Paolo
full_name: Giudici, Paolo
last_name: Giudici
- first_name: Giuseppe
full_name: Toscani, Giuseppe
last_name: Toscani
citation:
ama: Auricchio G, Brigati G, Giudici P, Toscani G. Multivariate Gini-type discrepancies.
Mathematical Models and Methods in Applied Sciences. 2025;35(5):1267-1296.
doi:10.1142/s0218202525500174
apa: Auricchio, G., Brigati, G., Giudici, P., & Toscani, G. (2025). Multivariate
Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences.
World Scientific Publishing. https://doi.org/10.1142/s0218202525500174
chicago: Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani.
“Multivariate Gini-Type Discrepancies.” Mathematical Models and Methods in
Applied Sciences. World Scientific Publishing, 2025. https://doi.org/10.1142/s0218202525500174.
ieee: G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “Multivariate Gini-type
discrepancies,” Mathematical Models and Methods in Applied Sciences, vol.
35, no. 5. World Scientific Publishing, pp. 1267–1296, 2025.
ista: Auricchio G, Brigati G, Giudici P, Toscani G. 2025. Multivariate Gini-type
discrepancies. Mathematical Models and Methods in Applied Sciences. 35(5), 1267–1296.
mla: Auricchio, Gennaro, et al. “Multivariate Gini-Type Discrepancies.” Mathematical
Models and Methods in Applied Sciences, vol. 35, no. 5, World Scientific Publishing,
2025, pp. 1267–96, doi:10.1142/s0218202525500174.
short: G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and
Methods in Applied Sciences 35 (2025) 1267–1296.
date_created: 2025-04-15T13:34:00Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2025-09-30T11:36:56Z
day: '01'
department:
- _id: JaMa
doi: 10.1142/s0218202525500174
external_id:
arxiv:
- '2411.01052'
isi:
- '001456337300001'
intvolume: ' 35'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2411.01052
month: '05'
oa: 1
oa_version: Preprint
page: 1267-1296
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multivariate Gini-type discrepancies
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 35
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19625'
abstract:
- lang: eng
text: We introduce operator-valued twisted Araki–Woods algebras. These are operator-valued
versions of a class of second quantization algebras that includes q-Gaussian and
q-Araki–Woods algebras and also generalize Shlyakhtenko’s von Neumann algebras
generated by operator-valued semicircular variables. We develop a disintegration
theory that reduces the isomorphism type of operator-valued twisted Araki–Woods
algebras over type I factors to the scalar-valued case. Moreover, these algebras
come with a natural weight, and we characterize its modular theory. We also give
sufficient criteria that guarantee the factoriality of these algebras.
acknowledgement: "The authors want to thank the organizers of YMC*A 2023 in Leuven,
where this collaboration was conceived. They are grateful to Dan Voiculescu for
a valuable historical remark and to Zhiyuan Yang for raising the question if operator-valued
weights give rise to Tomita correspondences. R.K. was funded by IIT Kanpur through
the Institute Postdoctoral Fellowship. M. W. was funded by the Austrian Science
Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access,
the authors have applied a CC BY public copyright licence to any Author Accepted
Manuscript (AAM) version arising from this submission.\r\nOpen Access funding enabled
and organized by Projekt DEAL."
article_number: '110'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: R. Rahul
full_name: Kumar, R. Rahul
last_name: Kumar
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Kumar RR, Wirth M. Operator-valued twisted Araki–Woods algebras. Communications
in Mathematical Physics. 2025;406(5). doi:10.1007/s00220-025-05285-7
apa: Kumar, R. R., & Wirth, M. (2025). Operator-valued twisted Araki–Woods algebras.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-025-05285-7
chicago: Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods
Algebras.” Communications in Mathematical Physics. Springer Nature, 2025.
https://doi.org/10.1007/s00220-025-05285-7.
ieee: R. R. Kumar and M. Wirth, “Operator-valued twisted Araki–Woods algebras,”
Communications in Mathematical Physics, vol. 406, no. 5. Springer Nature,
2025.
ista: Kumar RR, Wirth M. 2025. Operator-valued twisted Araki–Woods algebras. Communications
in Mathematical Physics. 406(5), 110.
mla: Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.”
Communications in Mathematical Physics, vol. 406, no. 5, 110, Springer
Nature, 2025, doi:10.1007/s00220-025-05285-7.
short: R.R. Kumar, M. Wirth, Communications in Mathematical Physics 406 (2025).
corr_author: '1'
date_created: 2025-04-27T22:02:13Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2025-09-30T12:19:22Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00220-025-05285-7
external_id:
arxiv:
- '2406.06179'
isi:
- '001464170400003'
pmid:
- '40225194'
file:
- access_level: open_access
checksum: 2948e8f567f20f5f837061d2c775534f
content_type: application/pdf
creator: dernst
date_created: 2025-05-05T09:20:54Z
date_updated: 2025-05-05T09:20:54Z
file_id: '19650'
file_name: 2025_CommMathPhysics_Kumar.pdf
file_size: 650764
relation: main_file
success: 1
file_date_updated: 2025-05-05T09:20:54Z
has_accepted_license: '1'
intvolume: ' 406'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Operator-valued twisted Araki–Woods algebras
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: 406
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '21322'
abstract:
- lang: eng
text: Habitat fragmentation poses a significant risk to population survival, causing
both demographic stochasticity and genetic drift within local populations to increase,
thereby increasing genetic load. Higher load causes population numbers to decline,
which reduces the efficiency of selection and further increases load, resulting
in a positive feedback that may drive entire populations to extinction. Here,
we investigate this eco-evolutionary feedback in a metapopulation consisting of
local demes connected via migration, with individuals subject to deleterious mutation
at a large number of loci. We first analyze the determinants of load under soft
selection, where population sizes are fixed, and then build on this to understand
hard selection, where population sizes and load coevolve. We show that under soft
selection, very little gene flow (less than one migrant per generation) is enough
to prevent fixation of deleterious alleles. By contrast, much higher levels of
migration are required to mitigate load and prevent extinction when selection
is hard, with critical migration thresholds for metapopulation persistence increasing
sharply as the genome-wide deleterious mutation rate becomes comparable to the
baseline population growth rate. Moreover, critical migration thresholds are highest
if deleterious mutations have intermediate selection coefficients but lower if
alleles are predominantly recessive rather than additive (due to more efficient
purging of recessive load within local populations). Our analysis is based on
a combination of analytical approximations and simulations, allowing for a more
comprehensive understanding of the factors influencing load and extinction in
fragmented populations.
acknowledgement: 'This research was partially funded by the Austrian Science Fund
(FWF P-32896B) and DOC Fellowships of the Austrian Academy of Sciences: grants 26380
(O.O.) and 26293 (K.K.). We thank Nick Barton for useful comments on the chapter
in O.O.’s thesis that led to this article.'
article_processing_charge: No
article_type: original
author:
- first_name: Oluwafunmilola O
full_name: Olusanya, Oluwafunmilola O
id: 41AD96DC-F248-11E8-B48F-1D18A9856A87
last_name: Olusanya
orcid: 0000-0003-1971-8314
- first_name: Kseniia
full_name: Khudiakova, Kseniia
id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
last_name: Khudiakova
orcid: 0000-0002-6246-1465
- first_name: Himani
full_name: Sachdeva, Himani
id: 42377A0A-F248-11E8-B48F-1D18A9856A87
last_name: Sachdeva
citation:
ama: Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback,
and extinction in metapopulations. The American Naturalist. 2025;205(6):617-636.
doi:10.1086/735562
apa: Olusanya, O. O., Khudiakova, K., & Sachdeva, H. (2025). Genetic load, eco-evolutionary
feedback, and extinction in metapopulations. The American Naturalist. University
of Chicago Press. https://doi.org/10.1086/735562
chicago: Olusanya, Oluwafunmilola O, Kseniia Khudiakova, and Himani Sachdeva. “Genetic
Load, Eco-Evolutionary Feedback, and Extinction in Metapopulations.” The American
Naturalist. University of Chicago Press, 2025. https://doi.org/10.1086/735562.
ieee: O. O. Olusanya, K. Khudiakova, and H. Sachdeva, “Genetic load, eco-evolutionary
feedback, and extinction in metapopulations,” The American Naturalist,
vol. 205, no. 6. University of Chicago Press, pp. 617–636, 2025.
ista: Olusanya OO, Khudiakova K, Sachdeva H. 2025. Genetic load, eco-evolutionary
feedback, and extinction in metapopulations. The American Naturalist. 205(6),
617–636.
mla: Olusanya, Oluwafunmilola O., et al. “Genetic Load, Eco-Evolutionary Feedback,
and Extinction in Metapopulations.” The American Naturalist, vol. 205,
no. 6, University of Chicago Press, 2025, pp. 617–36, doi:10.1086/735562.
short: O.O. Olusanya, K. Khudiakova, H. Sachdeva, The American Naturalist 205 (2025)
617–636.
corr_author: '1'
date_created: 2026-02-18T10:47:18Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2026-04-07T08:45:14Z
day: '01'
department:
- _id: JaMa
- _id: NiBa
doi: 10.1086/735562
external_id:
pmid:
- '40446297 '
intvolume: ' 205'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1101/2023.12.02.569702
month: '06'
oa: 1
oa_version: Preprint
page: 617-636
pmid: 1
project:
- _id: c08d3278-5a5b-11eb-8a69-fdb09b55f4b8
grant_number: P32896
name: Causes and consequences of population fragmentation
- _id: 34c872fe-11ca-11ed-8bc3-8534b82131e6
grant_number: '26380'
name: Polygenic Adaptation in a Metapopulation
- _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8
grant_number: '26293'
name: The impact of deleterious mutations on small populations
publication: The American Naturalist
publication_identifier:
eissn:
- 1537-5323
issn:
- 0003-0147
publication_status: published
publisher: University of Chicago Press
quality_controlled: '1'
related_material:
record:
- id: '14732'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Genetic load, eco-evolutionary feedback, and extinction in metapopulations
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 205
year: '2025'
...
---
OA_place: publisher
_id: '20563'
abstract:
- lang: eng
text: "The theory of optimal transport provides an elegant and powerful description
of many evolution\r\nequations as gradient flows. The primary objective of this
thesis is to adapt and extend the\r\ntheory to deal with important equations that
are not covered by the classical framework,\r\nspecifically boundary value problems
and kinetic equations. Additionally, we establish new\r\nresults in periodic homogenization
for discrete dynamical optimal transport and in quantization\r\nof measures.\r\nSection
1.1 serves as an invitation to the classical theory of optimal transport, including
the\r\nmain definitions and a selection of well-established theorems. Sections
1.2-1.5 introduce the\r\nmain results of this thesis, outline the motivations,
and review the current state of the art.\r\nIn Chapter 2, we consider the Fokker–Planck
equation on a bounded set with positive Dirichlet\r\nboundary conditions. We construct
a time-discrete scheme involving a modification of the\r\nWasserstein distance
and, under weak assumptions, prove its convergence to a solution of this\r\nboundary
value problem. In dimension 1, we show that this solution is a gradient flow in
a\r\nsuitable space of measures.\r\nChapter 3 presents joint work with Giovanni
Brigati and Jan Maas. We introduce a new theory\r\nof optimal transport to describe
and study particle systems at the mesoscopic scale. We prove\r\nadapted versions
of some fundamental theorems, including the Benamou–Brenier formula and\r\nthe
identification of absolutely continuous curves of measures.\r\nChapter 4 presents
joint work with Lorenzo Portinale. We prove convergence of dynamical\r\ntransportation
functionals on periodic graphs in the large-scale limit when the cost functional\r\nis
asymptotically linear. Additionally, we show that discrete 1-Wasserstein distances
converge\r\nto 1-Wasserstein distances constructed from crystalline norms on R\r\nd\r\n.\r\nChapter
5 concerns optimal empirical quantization: the problem of approximating a measure\r\nby
the sum of n equally weighted Dirac deltas, so as to minimize the error in the
p-Wasserstein\r\ndistance. Our main result is an analog of Zador’s theorem, providing
asymptotic bounds for\r\nthe minimal error as n tends to infinity.\r\n"
acknowledgement: "The research contained in this thesis has received funding from
the Austrian Science\r\nFund (FWF) project 10.55776/F65."
alternative_title:
- ISTA Thesis
article_processing_charge: No
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. Optimal transport methods for kinetic equations, boundary value
problems, and discretization of measures. 2025. doi:10.15479/AT-ISTA-20563
apa: Quattrocchi, F. (2025). Optimal transport methods for kinetic equations,
boundary value problems, and discretization of measures. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT-ISTA-20563
chicago: Quattrocchi, Filippo. “Optimal Transport Methods for Kinetic Equations,
Boundary Value Problems, and Discretization of Measures.” Institute of Science
and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20563.
ieee: F. Quattrocchi, “Optimal transport methods for kinetic equations, boundary
value problems, and discretization of measures,” Institute of Science and Technology
Austria, 2025.
ista: Quattrocchi F. 2025. Optimal transport methods for kinetic equations, boundary
value problems, and discretization of measures. Institute of Science and Technology
Austria.
mla: Quattrocchi, Filippo. Optimal Transport Methods for Kinetic Equations, Boundary
Value Problems, and Discretization of Measures. Institute of Science and Technology
Austria, 2025, doi:10.15479/AT-ISTA-20563.
short: F. Quattrocchi, Optimal Transport Methods for Kinetic Equations, Boundary
Value Problems, and Discretization of Measures, Institute of Science and Technology
Austria, 2025.
corr_author: '1'
date_created: 2025-10-28T13:10:49Z
date_published: 2025-11-03T00:00:00Z
date_updated: 2026-04-07T12:39:35Z
day: '03'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/AT-ISTA-20563
file:
- access_level: open_access
checksum: 6f55275bdf99992be3a6457d949dd664
content_type: application/pdf
creator: fquattro
date_created: 2025-11-17T21:04:15Z
date_updated: 2026-01-01T23:30:03Z
embargo: 2026-01-01
file_id: '20653'
file_name: 2025_quattrocchi_filippo_thesis.pdf
file_size: 4326411
relation: main_file
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creator: fquattro
date_created: 2025-11-17T21:05:43Z
date_updated: 2026-01-01T23:30:03Z
embargo_to: open_access
file_id: '20654'
file_name: 2025_quattrocchi_thesis.zip
file_size: 11726509
relation: source_file
file_date_updated: 2026-01-01T23:30:03Z
has_accepted_license: '1'
keyword:
- optimal transport
- kinetic equations
- boundary value problems
- quantization
- gradient flows
- homogenization
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: '240'
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '18706'
relation: part_of_dissertation
status: public
- id: '20569'
relation: part_of_dissertation
status: public
- id: '20571'
relation: part_of_dissertation
status: public
- id: '20570'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Optimal transport methods for kinetic equations, boundary value problems, and
discretization of measures
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
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: 2026-04-29T22:30:16Z
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: '18158'
abstract:
- lang: eng
text: "We study the geometry of Poisson point processes from the point of view of
optimal transport and Ricci lower bounds. We construct a Riemannian structure
on the space of point processes and the associated distance W that corresponds
to the Benamou–Brenier variational formula. Our main tool is a non-local continuity
equation formulated with the difference operator. The closure of the domain of
the relative entropy is a complete geodesic space, when endowed with \r\nW. The
geometry of this non-local infinite-dimensional space is analogous to that of
spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck
semi-group is the gradient flow of the relative entropy; (b) the Poisson space
has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI
inequality."
- lang: fre
text: "Nous étudions la géométrie des processus ponctuels de Poisson à travers le
prisme du transport optimal et de la minoration de la courbure de Ricci. Nous
construisons une structure\r\nriemannienne sur l’espace des processus ponctuels
et la distance associée W qui concorde avec la formulation variationnelle de Benamou–Brenier.
Notre analyse repose sur une équation de continuité non locale définie à l’aide
de l’opérateur de différence. La fermeture du domaine de l’entropie relative,
équipé de W, est un espace géodésique complet. La géométrie de cet espace non
local et de dimension infinie est analogue à celle des espaces à courbure de Ricci
strictement positive. Entre autres : (a) le semi-groupe d’Ornstein–Uhlenbeck est
le flot du gradient de l’entropie relative ; (b) l’espace de Poisson a une courbure
de Ricci entropique minorée par 1 ; (c) W satisfait une inégalité HWI."
article_processing_charge: Yes
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: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Herry R, Suzuki K. Wasserstein geometry and Ricci curvature
bounds for Poisson spaces. Journal de l’Ecole Polytechnique - Mathematiques.
2024;11:957-1010. doi:10.5802/jep.270
apa: Dello Schiavo, L., Herry, R., & Suzuki, K. (2024). Wasserstein geometry
and Ricci curvature bounds for Poisson spaces. Journal de l’Ecole Polytechnique
- Mathematiques. Ecole Polytechnique. https://doi.org/10.5802/jep.270
chicago: Dello Schiavo, Lorenzo, Ronan Herry, and Kohei Suzuki. “Wasserstein Geometry
and Ricci Curvature Bounds for Poisson Spaces.” Journal de l’Ecole Polytechnique
- Mathematiques. Ecole Polytechnique, 2024. https://doi.org/10.5802/jep.270.
ieee: L. Dello Schiavo, R. Herry, and K. Suzuki, “Wasserstein geometry and Ricci
curvature bounds for Poisson spaces,” Journal de l’Ecole Polytechnique - Mathematiques,
vol. 11. Ecole Polytechnique, pp. 957–1010, 2024.
ista: Dello Schiavo L, Herry R, Suzuki K. 2024. Wasserstein geometry and Ricci curvature
bounds for Poisson spaces. Journal de l’Ecole Polytechnique - Mathematiques. 11,
957–1010.
mla: Dello Schiavo, Lorenzo, et al. “Wasserstein Geometry and Ricci Curvature Bounds
for Poisson Spaces.” Journal de l’Ecole Polytechnique - Mathematiques,
vol. 11, Ecole Polytechnique, 2024, pp. 957–1010, doi:10.5802/jep.270.
short: L. Dello Schiavo, R. Herry, K. Suzuki, Journal de l’Ecole Polytechnique -
Mathematiques 11 (2024) 957–1010.
corr_author: '1'
date_created: 2024-09-29T22:01:38Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2025-09-08T09:50:50Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.5802/jep.270
external_id:
arxiv:
- '2303.00398'
isi:
- '001367254000003'
file:
- access_level: open_access
checksum: 5a51da5fb5f7fcaada378d43444cced8
content_type: application/pdf
creator: dernst
date_created: 2024-10-01T07:31:56Z
date_updated: 2024-10-01T07:31:56Z
file_id: '18164'
file_name: 2024_JourEcolePolytechniqueMath_DelloSchiavo.pdf
file_size: 1250553
relation: main_file
success: 1
file_date_updated: 2024-10-01T07:31:56Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 957-1010
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_identifier:
eissn:
- 2270-518X
issn:
- 2429-7100
publication_status: published
publisher: Ecole Polytechnique
quality_controlled: '1'
scopus_import: '1'
status: public
title: Wasserstein geometry and Ricci curvature bounds for Poisson spaces
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: 11
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
date_updated: 2024-11-04T08:54:26Z
file_id: '18497'
file_name: 2024_JourLondonMathSoc_Schiavo.pdf
file_size: 911476
relation: main_file
success: 1
file_date_updated: 2024-11-04T08:54:26Z
has_accepted_license: '1'
intvolume: ' 110'
isi: 1
issue: '5'
language:
- iso: eng
month: '11'
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'
...
---
_id: '13271'
abstract:
- lang: eng
text: "In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor
parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite
matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions
of trace functionals of this type. As applications, we extend some results in
Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res
Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński
(Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix
setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum
Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that
some related trace functionals are not concave in general. Such concavity results
were expected to hold in different problems."
acknowledgement: I am grateful to Boguslaw Zegarliński for asking me the questions
in [3] and for helpful communication. I also want to thank Paata Ivanisvili for
drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous
referee for the valuable comments and for pointing out some errors in an earlier
version of the paper. This work is partially supported by the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Zhang H. Some convexity and monotonicity results of trace functionals. Annales
Henri Poincare. 2024;25:2087-2106. doi:10.1007/s00023-023-01345-7
apa: Zhang, H. (2024). Some convexity and monotonicity results of trace functionals.
Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-023-01345-7
chicago: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.”
Annales Henri Poincare. Springer Nature, 2024. https://doi.org/10.1007/s00023-023-01345-7.
ieee: H. Zhang, “Some convexity and monotonicity results of trace functionals,”
Annales Henri Poincare, vol. 25. Springer Nature, pp. 2087–2106, 2024.
ista: Zhang H. 2024. Some convexity and monotonicity results of trace functionals.
Annales Henri Poincare. 25, 2087–2106.
mla: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.”
Annales Henri Poincare, vol. 25, Springer Nature, 2024, pp. 2087–106, doi:10.1007/s00023-023-01345-7.
short: H. Zhang, Annales Henri Poincare 25 (2024) 2087–2106.
corr_author: '1'
date_created: 2023-07-23T22:01:15Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-04-14T07:43:55Z
day: '01'
department:
- _id: JaMa
doi: 10.1007/s00023-023-01345-7
ec_funded: 1
external_id:
arxiv:
- '2108.05785'
isi:
- '001025709100001'
intvolume: ' 25'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2108.05785
month: '04'
oa: 1
oa_version: Preprint
page: 2087-2106
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Some convexity and monotonicity results of trace functionals
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2024'
...
---
_id: '13318'
abstract:
- lang: eng
text: Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free
constants that grow subexponentially in the degree (Defant et al. in Math Ann
374(1):653–680, 2019). Such inequalities have found great applications in learning
low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th
annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated
by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality
for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand,
KKL and Friedgut’s theorems and the learnability of quantum Boolean functions,
2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et
al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894).
In this paper, we give a new proof of these Bohnenblust–Hille inequalities for
qubit system with constants that are dimension-free and of exponential growth
in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials.
Using similar ideas, we also study learning problems of low degree quantum observables
and Bohr’s radius phenomenon on quantum Boolean cubes.
acknowledgement: The research of A.V. is supported by NSF DMS-1900286, DMS-2154402
and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship,
Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284
while both authors were in residence at the Institute for Computational and Experimental
Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity
program.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Alexander
full_name: Volberg, Alexander
last_name: Volberg
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. Mathematische
Annalen. 2024;389:1657-1676. doi:10.1007/s00208-023-02680-0
apa: Volberg, A., & Zhang, H. (2024). Noncommutative Bohnenblust–Hille inequalities.
Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-023-02680-0
chicago: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille
Inequalities.” Mathematische Annalen. Springer Nature, 2024. https://doi.org/10.1007/s00208-023-02680-0.
ieee: A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,”
Mathematische Annalen, vol. 389. Springer Nature, pp. 1657–1676, 2024.
ista: Volberg A, Zhang H. 2024. Noncommutative Bohnenblust–Hille inequalities. Mathematische
Annalen. 389, 1657–1676.
mla: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.”
Mathematische Annalen, vol. 389, Springer Nature, 2024, pp. 1657–76, doi:10.1007/s00208-023-02680-0.
short: A. Volberg, H. Zhang, Mathematische Annalen 389 (2024) 1657–1676.
corr_author: '1'
date_created: 2023-07-30T22:01:03Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-04-23T07:50:55Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-023-02680-0
external_id:
arxiv:
- '2210.14468'
isi:
- '001035665500001'
pmid:
- '38751410'
file:
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checksum: 56e67756e4c6c97589a8385e15ea2d2a
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creator: dernst
date_created: 2024-07-22T09:38:15Z
date_updated: 2024-07-22T09:38:15Z
file_id: '17299'
file_name: 2024_MathAnnalen_Volberg.pdf
file_size: 351796
relation: main_file
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month: '06'
oa: 1
oa_version: Published Version
page: 1657-1676
pmid: 1
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Noncommutative Bohnenblust–Hille inequalities
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: 389
year: '2024'
...
---
OA_place: publisher
OA_type: gold
_id: '18897'
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
day: '01'
ddc:
- '000'
department:
- _id: JaMa
- _id: MaMo
external_id:
arxiv:
- '2305.14164'
file:
- access_level: open_access
checksum: 76a1fd5afd8ee6f7ae0e5912d7dbf6b4
content_type: application/pdf
creator: dernst
date_created: 2025-01-27T12:19:44Z
date_updated: 2025-01-27T12:19:44Z
file_id: '18898'
file_name: 2024_TMLR_Pedrotti.pdf
file_size: 780315
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