---
OA_place: publisher
OA_type: hybrid
_id: '18632'
abstract:
- lang: eng
text: 'For an arbitrary dimension (Formula presented.), we study: the polyharmonic
Gaussian field (Formula presented.) on the discrete torus (Formula presented.),
that is the random field whose law on (Formula presented.) given by (Formula presented.)
where (Formula presented.) is the Lebesgue measure and (Formula presented.) is
the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG)
measure associated with it, that is, the random measure on (Formula presented.)
(Formula presented.) where (Formula presented.) is a regularity parameter. As
(Formula presented.), we prove convergence of the fields (Formula presented.)
to the polyharmonic Gaussian field (Formula presented.) on the continuous torus
(Formula presented.), as well as convergence of the random measures (Formula presented.)
to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula
presented.). '
acknowledgement: "KTS is grateful to Christoph Thiele for valuable discussions and
helpful references. LDS is grateful to Nathanaël Berestycki for valuable discussions
on Gaussian Multiplicative Chaoses. The authors are grateful to an anonymous reviewer
for suggestions which improved the presentation.\r\nThe authors gratefully acknowledge
funding by the Deutsche Forschungsgemeinschaft through the project ‘Random Riemannian
Geometry’ within the SPP 2265 ‘Random Geometric Systems.'\r\nLDS gratefully acknowledges
financial support from the European Research Council (grant agreement No. 716117,
awarded to J. Maas) and from the Austrian Science Fund (FWF). His research was funded
by the Austrian Science Fund (FWF) project 10.55776/F65 and project 10.55776/ESP208.\r\nRH,
EK, and KTS gratefully acknowledge funding by the Hausdorff Center for Mathematics
(project ID 390685813), and through project B03 within the CRC 1060 (project ID
211504053). RH and KTS also gratefully acknowledges financial support from the European
Research Council through the ERC AdG ‘RicciBounds’ (grant agreement 694405).\r\nOpen
access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Ronan
full_name: Herry, Ronan
last_name: Herry
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: 'Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville
quantum gravity measures on tori of arbitrary dimension: From discrete to continuous.
Mathematische Nachrichten. 2025;298(1):244-281. doi:10.1002/mana.202400169'
apa: 'Dello Schiavo, L., Herry, R., Kopfer, E., & Sturm, K. T. (2025). Polyharmonic
fields and Liouville quantum gravity measures on tori of arbitrary dimension:
From discrete to continuous. Mathematische Nachrichten. Wiley. https://doi.org/10.1002/mana.202400169'
chicago: 'Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm.
“Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary
Dimension: From Discrete to Continuous.” Mathematische Nachrichten. Wiley,
2025. https://doi.org/10.1002/mana.202400169.'
ieee: 'L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields
and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete
to continuous,” Mathematische Nachrichten, vol. 298, no. 1. Wiley, pp.
244–281, 2025.'
ista: 'Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2025. Polyharmonic fields and
Liouville quantum gravity measures on tori of arbitrary dimension: From discrete
to continuous. Mathematische Nachrichten. 298(1), 244–281.'
mla: 'Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum
Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.”
Mathematische Nachrichten, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:10.1002/mana.202400169.'
short: L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten
298 (2025) 244–281.
date_created: 2024-12-08T23:01:56Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1002/mana.202400169
ec_funded: 1
external_id:
arxiv:
- '2302.02963'
isi:
- '001366948500001'
file:
- access_level: open_access
checksum: 1dc50d156feb777c86d779fb1c9ac875
content_type: application/pdf
creator: dernst
date_created: 2025-01-13T10:34:42Z
date_updated: 2025-01-13T10:34:42Z
file_id: '18838'
file_name: 2025_MathNachrichten_DelloSchiavo.pdf
file_size: 1734511
relation: main_file
success: 1
file_date_updated: 2025-01-13T10:34:42Z
has_accepted_license: '1'
intvolume: ' 298'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 244-281
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Mathematische Nachrichten
publication_identifier:
eissn:
- 1522-2616
issn:
- 0025-584X
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary
dimension: From discrete to continuous'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 298
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14934'
abstract:
- lang: eng
text: "We study random perturbations of a Riemannian manifold (M, g) by means of
so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the
given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the
conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular
case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated
Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric
and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion,
spectral bound, or spectral gap change under the influence of the noise. And if
so, is\r\nit possible to quantify these dependencies in terms of key parameters
of the noise? Another\r\ngoal is to define and analyze in detail the Fractional
Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent
interest."
acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for
valuable discussions on this project. They are also grateful to Nathanaël Berestycki,
and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24],
and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous
version of the proof of Proposition 3.10. The authors feel very much indebted to
an anonymous reviewer for his/her careful reading and the many valuable suggestions
that have significantly contributed to the improvement of the paper. L.D.S. gratefully
acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC
1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65
at Institute of Science and Technology Austria. This research was funded in whole
or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open
access, the authors have applied a CC BY public copyright licence to any Author
Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff
Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian
geometry. Potential Analysis. 2024;61:501-553. doi:10.1007/s11118-023-10118-0
apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour
in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0
chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery
Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature,
2024. https://doi.org/10.1007/s11118-023-10118-0.
ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random
Riemannian geometry,” Potential Analysis, vol. 61. Springer Nature, pp.
501–553, 2024.
ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian
geometry. Potential Analysis. 61, 501–553.
mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.”
Potential Analysis, vol. 61, Springer Nature, 2024, pp. 501–53, doi:10.1007/s11118-023-10118-0.
short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis 61 (2024) 501–553.
date_created: 2024-02-04T23:00:54Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T11:57:14Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-023-10118-0
external_id:
arxiv:
- '2012.06796'
isi:
- '001151118800001'
file:
- access_level: open_access
checksum: 33c688bdf296c3d8f8bbd96c7dd26037
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:13:34Z
date_updated: 2025-01-09T08:13:34Z
file_id: '18789'
file_name: 2024_PotentialAnalysis_DelloSchiavo.pdf
file_size: 1294993
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:13:34Z
has_accepted_license: '1'
intvolume: ' 61'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 501-553
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A discovery tour in random Riemannian geometry
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 61
year: '2024'
...
---
_id: '15252'
abstract:
- lang: eng
text: A measurable map between measure spaces is shown to have bounded compression
if and only if its image via the measure-algebra functor is Lipschitz-continuous
w.r.t. the measure-algebra distances. This provides a natural interpretation of
maps of bounded compression/deformation by means of the measure-algebra functor
and corrobo-rates the assertion that maps of bounded deformation are a natural
class of morphisms for the category of complete and separable metric measure spaces.
acknowledgement: "The author gratefully acknowledges funding of his current position
by the Austrian Science\r\nFund (FWF), grant ESPRIT208. He is grateful to Enrico
Pasqualetto for pointing out some\r\nreferences on maps of bounded compression."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. A characterization of maps of bounded compression. Mathematical
Communications. 2024;29(1):137-142.
apa: Dello Schiavo, L. (2024). A characterization of maps of bounded compression.
Mathematical Communications. Udruga Matematicara Osijek.
chicago: Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.”
Mathematical Communications. Udruga Matematicara Osijek, 2024.
ieee: L. Dello Schiavo, “A characterization of maps of bounded compression,” Mathematical
Communications, vol. 29, no. 1. Udruga Matematicara Osijek, pp. 137–142, 2024.
ista: Dello Schiavo L. 2024. A characterization of maps of bounded compression.
Mathematical Communications. 29(1), 137–142.
mla: Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.”
Mathematical Communications, vol. 29, no. 1, Udruga Matematicara Osijek,
2024, pp. 137–42.
short: L. Dello Schiavo, Mathematical Communications 29 (2024) 137–142.
corr_author: '1'
date_created: 2024-03-31T22:01:12Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2025-04-14T12:59:08Z
day: '01'
department:
- _id: JaMa
external_id:
arxiv:
- '2304.11348'
intvolume: ' 29'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2304.11348
month: '01'
oa: 1
oa_version: Preprint
page: 137-142
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Mathematical Communications
publication_identifier:
eissn:
- 1848-8013
issn:
- 1331-0623
publication_status: published
publisher: Udruga Matematicara Osijek
quality_controlled: '1'
scopus_import: '1'
status: public
title: A characterization of maps of bounded compression
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2024'
...
---
_id: '15317'
abstract:
- lang: eng
text: 'We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes
on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random
walks on Ω dual to SEP/SIP we establish: a functional-CLT-type convergence to
the Brownian motion on Ω with either Neumann (slow boundary), Dirichlet (fast
boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum
convergence of the corresponding harmonic profiles. As a consequence, we rigorously
derive the hydrodynamic and hydrostatic limits for SEP/SIP on Ω, and analyze their
stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP
concern finite-dimensional distribution convergence only, as our duality techniques
do not require to establish tightness for the fields associated to the particle
systems.'
acknowledgement: "The first author gratefully acknowledges funding by the Austrian
Science Fund (FWF) grant F65, by the European Research Council (ERC, grant agreement
No 716117, awarded to Prof. Dr. Jan Maas). He also gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) grant ESPRIT 208.\r\nThe
second author gratefully acknowledges funding by the Hausdorff Center for Mathematics
at the University of Bonn. Part of this work was completed while this author was
a member of the Institute of Science and Technology Austria. He gratefully acknowledges
funding of his position at that time by the Austrian Science Fund (FWF) grants F65
and W1245.\r\nThe third author gratefully acknowledges funding by the Lise Meitner
fellowship, Austrian Science Fund (FWF): M3211. Part of this work was completed
while funded by the European Union’s Horizon 2020 research and innovation programme
under the Marie-Skłodowska-Curie grant agreement No. 754411."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Dello Schiavo L, Portinale L, Sau F. Scaling limits of random walks, harmonic
profiles, and stationary nonequilibrium states in Lipschitz domains. Annals
of Applied Probability. 2024;34(2):1789-1845. doi:10.1214/23-AAP2007
apa: Dello Schiavo, L., Portinale, L., & Sau, F. (2024). Scaling limits of random
walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains.
Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2007
chicago: Dello Schiavo, Lorenzo, Lorenzo Portinale, and Federico Sau. “Scaling Limits
of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz
Domains.” Annals of Applied Probability. Institute of Mathematical Statistics,
2024. https://doi.org/10.1214/23-AAP2007.
ieee: L. Dello Schiavo, L. Portinale, and F. Sau, “Scaling limits of random walks,
harmonic profiles, and stationary nonequilibrium states in Lipschitz domains,”
Annals of Applied Probability, vol. 34, no. 2. Institute of Mathematical
Statistics, pp. 1789–1845, 2024.
ista: Dello Schiavo L, Portinale L, Sau F. 2024. Scaling limits of random walks,
harmonic profiles, and stationary nonequilibrium states in Lipschitz domains.
Annals of Applied Probability. 34(2), 1789–1845.
mla: Dello Schiavo, Lorenzo, et al. “Scaling Limits of Random Walks, Harmonic Profiles,
and Stationary Nonequilibrium States in Lipschitz Domains.” Annals of Applied
Probability, vol. 34, no. 2, Institute of Mathematical Statistics, 2024, pp.
1789–845, doi:10.1214/23-AAP2007.
short: L. Dello Schiavo, L. Portinale, F. Sau, Annals of Applied Probability 34
(2024) 1789–1845.
corr_author: '1'
date_created: 2024-04-14T22:01:02Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-09-04T13:36:00Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/23-AAP2007
ec_funded: 1
external_id:
arxiv:
- '2112.14196'
isi:
- '001198623200016'
intvolume: ' 34'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2112.14196
month: '04'
oa: 1
oa_version: Preprint
page: 1789-1845
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 3490b268-11ca-11ed-8bc3-e0ad03f48839
grant_number: M03211
name: Reaching consensus in heterogeneous random opinion dynamics
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1245
name: Dissipation and dispersion in nonlinear partial differential equations
publication: Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium
states in Lipschitz domains
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 34
year: '2024'
...
---
_id: '17143'
abstract:
- lang: eng
text: "This paper deals with local criteria for the convergence to a global minimiser
for gradient flow trajectories and their discretisations. To obtain quantitative
estimates on the speed of convergence, we consider variations on the classical
Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions
are given in terms of the initial data, without any reference to an equilibrium
point. The main results are convergence statements for gradient flow curves and
proximal point sequences to a global minimiser, together with sharp quantitative
estimates on the speed of convergence. These convergence results apply in the
general setting of lower semicontinuous functionals on complete metric spaces,
generalising recent results for smooth functionals on Rn. While the non-smooth
setting covers very general spaces, it is also useful for (non)-smooth functionals
on Rn.\r\n."
acknowledgement: The authors gratefully acknowledges support by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No. 716117). This research was funded in part by the Austrian Science
Fund (FWF) project 10.55776/ESP208. This research was funded in part by the Austrian
Science Fund (FWF) project 10.55776/F65
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Francesco
full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence
of gradient flows and proximal point sequences in metric spaces. Transactions
of the American Mathematical Society. 2024;377(6):3779-3804. doi:10.1090/tran/9156
apa: Dello Schiavo, L., Maas, J., & Pedrotti, F. (2024). Local conditions for
global convergence of gradient flows and proximal point sequences in metric spaces.
Transactions of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/tran/9156
chicago: Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions
for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric
Spaces.” Transactions of the American Mathematical Society. American Mathematical
Society, 2024. https://doi.org/10.1090/tran/9156.
ieee: L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence
of gradient flows and proximal point sequences in metric spaces,” Transactions
of the American Mathematical Society, vol. 377, no. 6. American Mathematical
Society, pp. 3779–3804, 2024.
ista: Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence
of gradient flows and proximal point sequences in metric spaces. Transactions
of the American Mathematical Society. 377(6), 3779–3804.
mla: Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of
Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions
of the American Mathematical Society, vol. 377, no. 6, American Mathematical
Society, 2024, pp. 3779–804, doi:10.1090/tran/9156.
short: L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical
Society 377 (2024) 3779–3804.
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-04-07T13:00:02Z
day: '01'
department:
- _id: JaMa
doi: 10.1090/tran/9156
ec_funded: 1
external_id:
arxiv:
- '2304.05239'
isi:
- '001203273300001'
intvolume: ' 377'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2304.05239
month: '06'
oa: 1
oa_version: Preprint
page: 3779-3804
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
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grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Transactions of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6850
issn:
- 0002-9947
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
related_material:
record:
- id: '17336'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local conditions for global convergence of gradient flows and proximal point
sequences in metric spaces
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 377
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18490'
abstract:
- lang: eng
text: 'For large classes of even-dimensional Riemannian manifolds (Formula presented.),
we construct and analyze conformally invariant random fields. These centered Gaussian
fields (Formula presented.), called co-polyharmonic Gaussian fields, are characterized
by their covariance kernels k which exhibit a precise logarithmic divergence:
(Formula presented.). They share a fundamental quasi-invariance property under
conformal transformations. In terms of the co-polyharmonic Gaussian field (Formula
presented.), we define the Liouville Quantum Gravity measure, a random measure
on (Formula presented.), heuristically given as (Formula presented.) and rigorously
obtained as almost sure weak limit of the right-hand side with (Formula presented.)
replaced by suitable regular approximations (Formula presented.). In terms on
the Liouville Quantum Gravity measure, we define the Liouville Brownian motion
on (Formula presented.) and the random GJMS operators. Finally, we present an
approach to a conformal field theory in arbitrary even dimension with an ansatz
based on Branson''s (Formula presented.) -curvature: we give a rigorous meaning
to the Polyakov–Liouville measure (Formula presented.) and we derive the corresponding
conformal anomaly. The set of admissible manifolds is conformally invariant. It
includes all compact 2-dimensional Riemannian manifolds, all compact non-negatively
curved Einstein manifolds of even dimension, and large classes of compact hyperbolic
manifolds of even dimension. However, not every compact even-dimensional Riemannian
manifold is admissible. Our results concerning the logarithmic divergence of the
kernel (Formula presented.) rely on new sharp estimates for heat kernels and higher
order Green kernels on arbitrary closed manifolds. '
acknowledgement: The authors are grateful to Masha Gordina for helpful references,
and to Nathanaël Berestycki, Baptiste Cerclé, and Ewain Gwynne for valuable comments
on the first circulated version of this paper. They also would like to thank Sebastian
Andres, Peter Friz, and Yizheng Yuan for pointing out an erroneous formulation in
the previous version of Theorem 5.7. Moreover, KTS would liketo express his thanks
to Sebastian Andres, Matthias Erbar, Martin Huesmann, and Jan Mass for stimulating
discussions on previous attempts to this project. LDS gratefully acknowledges financial
support from the European Research Council (grant agreement No 716117, awarded to
J. Maas), from the Austrian Science Fund (FWF) project 10.55776/ESP208, and from
the Austrian Science Fund (FWF) project 10.55776/F65.RH, EK, and KTS gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the project “Random
Riemannian Geometry” within the SPP 2265 “Random Geomet-ric Systems,” through the
Hausdorff Center for Mathematics (project ID 390685813), and through project B03
within the CRC 1060 (project ID 211504053). RH and KTS also gratefully acknowledge
financial support from the European Research Council through the ERC AdG “RicciBounds”(grant
agreement 694405).Data sharing not applicable to this article as no datasets were
generated or analyzed during the current study. Open access funding enabled and
organized by Projekt DEAL.
article_number: e70003
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Ronan
full_name: Herry, Ronan
last_name: Herry
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Conformally invariant random
fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian
manifolds of even dimension. Journal of the London Mathematical Society.
2024;110(5). doi:10.1112/jlms.70003
apa: Dello Schiavo, L., Herry, R., Kopfer, E., & Sturm, K. T. (2024). Conformally
invariant random fields, Liouville quantum gravity measures, and random Paneitz
operators on Riemannian manifolds of even dimension. Journal of the London
Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.70003
chicago: Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm.
“Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and
Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” Journal
of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.70003.
ieee: L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Conformally invariant
random fields, Liouville quantum gravity measures, and random Paneitz operators
on Riemannian manifolds of even dimension,” Journal of the London Mathematical
Society, vol. 110, no. 5. London Mathematical Society, 2024.
ista: Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2024. Conformally invariant
random fields, Liouville quantum gravity measures, and random Paneitz operators
on Riemannian manifolds of even dimension. Journal of the London Mathematical
Society. 110(5), e70003.
mla: Dello Schiavo, Lorenzo, et al. “Conformally Invariant Random Fields, Liouville
Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds
of Even Dimension.” Journal of the London Mathematical Society, vol. 110,
no. 5, e70003, London Mathematical Society, 2024, doi:10.1112/jlms.70003.
short: L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Journal of the London
Mathematical Society 110 (2024).
date_created: 2024-11-03T23:01:44Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-08T14:29:45Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1112/jlms.70003
ec_funded: 1
external_id:
isi:
- '001351918100029'
file:
- access_level: open_access
checksum: 143816823b5f43bd3748da8e3e91cef5
content_type: application/pdf
creator: dernst
date_created: 2024-11-04T08:54:26Z
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: '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
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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'
...
---
_id: '12104'
abstract:
- lang: eng
text: We study ergodic decompositions of Dirichlet spaces under intertwining via
unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular
Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore,
every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces
is decomposable over their ergodic decompositions up to conjugation via an isomorphism
of the corresponding indexing spaces.
acknowledgement: Research supported by the Austrian Science Fund (FWF) grant F65 at
the Institute of Science and Technology Austria and by the European Research Council
(ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully
acknowledges funding of his current position by the Austrian Science Fund (FWF)
through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme
(Grant No. 156).
article_number: '9'
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: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order
isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7
apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet
forms under order isomorphisms. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00859-7
chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of
Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations.
Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.
ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms
under order isomorphisms,” Journal of Evolution Equations, vol. 23, no.
1. Springer Nature, 2023.
ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms
under order isomorphisms. Journal of Evolution Equations. 23(1), 9.
mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet
Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23,
no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.
short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).
corr_author: '1'
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2025-04-23T08:45:56Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00028-022-00859-7
ec_funded: 1
external_id:
isi:
- '000906214600004'
pmid:
- '36597554'
file:
- access_level: open_access
checksum: 1f34f3e2cb521033de6154f274ea3a4e
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creator: dernst
date_created: 2023-01-20T10:45:06Z
date_updated: 2023-01-20T10:45:06Z
file_id: '12325'
file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf
file_size: 422612
relation: main_file
success: 1
file_date_updated: 2023-01-20T10:45:06Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
pmid: 1
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: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decompositions of Dirichlet forms under order isomorphisms
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: 23
year: '2023'
...
---
_id: '13145'
abstract:
- lang: eng
text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary
finite diffuse measure space. We provide an interpretation of this characterization
in analogy with the Mecke identity for Poisson point processes.
acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects
(University of Bonn). L.D.S. gratefully acknowledges funding of his current position
by the Austrian Science Fund (FWF) through project ESPRIT 208.
article_processing_charge: No
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: Eugene
full_name: Lytvynov, Eugene
last_name: Lytvynov
citation:
ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528
apa: Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization
of the Dirichlet–Ferguson measure. Electronic Communications in Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528
chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528.
ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson
measure,” Electronic Communications in Probability, vol. 28. Institute
of Mathematical Statistics, pp. 1–12, 2023.
ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 28, 1–12.
mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability,
vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528.
short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28
(2023) 1–12.
corr_author: '1'
date_created: 2023-06-18T22:00:48Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2025-04-14T12:59:08Z
day: '05'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/23-ECP528
external_id:
isi:
- '001042025400001'
file:
- access_level: open_access
checksum: 4a543fe4b3f9e747cc52167c17bfb524
content_type: application/pdf
creator: dernst
date_created: 2023-06-19T09:37:40Z
date_updated: 2023-06-19T09:37:40Z
file_id: '13152'
file_name: 2023_ElectronCommProbability_Schiavo.pdf
file_size: 271434
relation: main_file
success: 1
file_date_updated: 2023-06-19T09:37:40Z
has_accepted_license: '1'
intvolume: ' 28'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1-12
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Electronic Communications in Probability
publication_identifier:
eissn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Mecke-type characterization of the Dirichlet–Ferguson measure
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: 28
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '20572'
abstract:
- lang: eng
text: "We present an elementary non-recursive formula for the multivariate moments\r\nof
the Dirichlet distribution on the standard simplex, in terms of the pattern\r\ninventory
of the moments' exponents. We obtain analog formulas for the\r\nmultivariate moments
of the Dirichlet-Ferguson and Gamma measures. We further\r\nintroduce a polychromatic
analogue of Ewens sampling formula on colored integer\r\npartitions, discuss its
relation with suitable extensions of Hoppe's urn model\r\nand of the Chinese restaurant
process, and prove that it satisfies an adapted\r\nnotion of consistency in the
sense of Kingman."
acknowledgement: This research was funded by the Austrian Science Fund (FWF) ESPRIT
208. For the purpose of open access, the authors have applied a CC BY public copyright
licence to any Author Accepted Manuscript version arising from this submission.
F.Q. gratefully acknowledges support by the Austrian Science Fund (FWF), Project
SFB F65. The authors are grateful to Professor Nathanaël Berestycki for several
helpful suggestions, and to Nicola Battisti and Dr. Elizabeth Hollwey for enlightening
discussions on DNA-methylation.
article_number: '2309.11292'
article_processing_charge: No
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: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic
Ewens sampling formula. arXiv. doi:10.48550/arXiv.2309.11292
apa: Dello Schiavo, L., & Quattrocchi, F. (n.d.). Multivariate Dirichlet moments
and a polychromatic Ewens sampling formula. arXiv. https://doi.org/10.48550/arXiv.2309.11292
chicago: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet
Moments and a Polychromatic Ewens Sampling Formula.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.11292.
ieee: L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a
polychromatic Ewens sampling formula,” arXiv. .
ista: Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic
Ewens sampling formula. arXiv, 2309.11292.
mla: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments
and a Polychromatic Ewens Sampling Formula.” ArXiv, 2309.11292, doi:10.48550/arXiv.2309.11292.
short: L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:13:08Z
date_published: 2023-09-20T00:00:00Z
date_updated: 2025-11-24T13:53:48Z
day: '20'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2309.11292
external_id:
arxiv:
- '2309.11292'
keyword:
- Dirichlet distribution
- Ewens sampling formula
- Hoppe urn model
- colored partitions
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2309.11292
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
status: public
title: Multivariate Dirichlet moments and a polychromatic Ewens sampling formula
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '10145'
abstract:
- lang: eng
text: We study direct integrals of quadratic and Dirichlet forms. We show that each
quasi-regular Dirichlet space over a probability space admits a unique representation
as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same
underlying topology. The same holds for each quasi-regular strongly local Dirichlet
space over a metrizable Luzin σ-finite Radon measure space, and admitting carré
du champ operator. In this case, the representation is only projectively unique.
acknowledgement: The author is grateful to Professors Sergio Albeverio and Andreas
Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the
present work, and for respectively pointing out the references [1, 13], and [3,
20]. Finally, he is especially grateful to an anonymous Reviewer for their very
careful reading and their suggestions which improved the readability of the paper.
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
citation:
ama: Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals
and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y
apa: Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y
chicago: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis. Springer Nature, 2023.
https://doi.org/10.1007/s11118-021-09951-y.
ieee: L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals
and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615,
2023.
ista: Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. 58, 573–615.
mla: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature,
2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.
short: L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.
corr_author: '1'
date_created: 2021-10-17T22:01:17Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2025-04-14T07:27:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-021-09951-y
ec_funded: 1
external_id:
arxiv:
- '2003.01366'
isi:
- '000704213400001'
file:
- access_level: open_access
checksum: 625526482be300ca7281c91c30d41725
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T09:18:59Z
date_updated: 2023-10-04T09:18:59Z
file_id: '14387'
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file_size: 806391
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month: '03'
oa: 1
oa_version: Published Version
page: 573-615
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _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
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decomposition of Dirichlet forms via direct integrals and applications
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: 58
year: '2023'
...
---
_id: '11354'
abstract:
- lang: eng
text: We construct a recurrent diffusion process with values in the space of probability
measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process
is associated with the Dirichlet form defined by integration of the Wasserstein
gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional
base spaces to the modified massive Arratia flow over the unit interval described
in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800).
Together with two different constructions of the process, we discuss its ergodicity,
invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.
acknowledgement: Research supported by the Sonderforschungsbereich 1060 and the Hausdorff
Center for Mathematics. The author gratefully acknowledges funding of his current
position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the
European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr.
Jan Maas).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648.
doi:10.1214/21-AOP1541
apa: Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of
probability measures over a closed Riemannian manifold. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541
chicago: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space
of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability.
Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.
ieee: L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold,” Annals of Probability, vol.
50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.
ista: Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.
mla: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability
Measures over a Closed Riemannian Manifold.” Annals of Probability, vol.
50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.
short: L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.
corr_author: '1'
date_created: 2022-05-08T22:01:44Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2025-04-14T07:27:47Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AOP1541
ec_funded: 1
external_id:
arxiv:
- '1811.11598'
isi:
- '000773518500005'
intvolume: ' 50'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1811.11598'
month: '03'
oa: 1
oa_version: Preprint
page: 591-648
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: Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dirichlet–Ferguson diffusion on the space of probability measures over
a closed Riemannian manifold
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2022'
...
---
_id: '12177'
abstract:
- lang: eng
text: Using elementary hyperbolic geometry, we give an explicit formula for the
contraction constant of the skinning map over moduli spaces of relatively acylindrical
hyperbolic manifolds.
acknowledgement: "The first author was partially supported by the National Science
Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted
by the Mathematical Sciences Research Institute in Berkeley, California, during
the Fall 2020 semester. The second author gratefully acknowledges funding by the
Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research
Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche
Forschungsgemeinschaft through the SPP 2265."
article_processing_charge: No
article_type: original
author:
- first_name: Tommaso
full_name: Cremaschi, Tommaso
last_name: Cremaschi
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings
of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134
apa: Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning
maps. Proceedings of the American Mathematical Society, Series B. American
Mathematical Society. https://doi.org/10.1090/bproc/134
chicago: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of
Skinning Maps.” Proceedings of the American Mathematical Society, Series B.
American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134.
ieee: T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,”
Proceedings of the American Mathematical Society, Series B, vol. 9, no.
43. American Mathematical Society, pp. 445–459, 2022.
ista: Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps.
Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.
mla: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning
Maps.” Proceedings of the American Mathematical Society, Series B, vol.
9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134.
short: T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical
Society, Series B 9 (2022) 445–459.
corr_author: '1'
date_created: 2023-01-12T12:12:17Z
date_published: 2022-11-02T00:00:00Z
date_updated: 2025-04-14T07:27:48Z
day: '02'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1090/bproc/134
ec_funded: 1
file:
- access_level: open_access
checksum: cb4a79937c1f60d4c329a10ee797f0d2
content_type: application/pdf
creator: dernst
date_created: 2023-01-26T13:02:07Z
date_updated: 2023-01-26T13:02:07Z
file_id: '12404'
file_name: 2022_ProceedingsAMS_Cremaschi.pdf
file_size: 326471
relation: main_file
success: 1
file_date_updated: 2023-01-26T13:02:07Z
has_accepted_license: '1'
intvolume: ' 9'
issue: '43'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 445-459
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
publication: Proceedings of the American Mathematical Society, Series B
publication_identifier:
issn:
- 2330-1511
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Effective contraction of Skinning maps
tmp:
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legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
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short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2022'
...
---
_id: '10588'
abstract:
- lang: eng
text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying
the quasi curvature-dimension condition recently introduced in Milman (Commun
Pure Appl Math, to appear). We provide several applications to properties of the
corresponding heat semigroup. In particular, under the additional assumption of
infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the
heat semigroup with respect to the distance, and prove the irreducibility of the
heat semigroup. These results apply in particular to large classes of (ideal)
sub-Riemannian manifolds.
acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions
on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor
Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino
Antonelli for reading a preliminary version of this work and for their valuable
comments and suggestions. Finally, they wish to express their gratitude to two anonymous
Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S.
gratefully acknowledges funding of his position by the Austrian Science Fund (FWF)
grant F65, and by the European Research Council (ERC, grant No. 716117, awarded
to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS
Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research
Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research
on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number
17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium."
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: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and
applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2
apa: Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on
QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property
on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature,
2022. https://doi.org/10.1007/s00208-021-02331-2.
ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces
and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp.
1815–1832, 2022.
ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces
and applications. Mathematische Annalen. 384, 1815–1832.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on
QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer
Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.
short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.
corr_author: '1'
date_created: 2022-01-02T23:01:35Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2025-04-14T07:27:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-021-02331-2
ec_funded: 1
external_id:
arxiv:
- '2110.05137'
isi:
- '000734150200001'
file:
- access_level: open_access
checksum: 2593abbf195e38efa93b6006b1e90eb1
content_type: application/pdf
creator: alisjak
date_created: 2022-01-03T11:08:31Z
date_updated: 2022-01-03T11:08:31Z
file_id: '10596'
file_name: 2021_MathAnn_DelloSchiavo.pdf
file_size: 410090
relation: main_file
success: 1
file_date_updated: 2022-01-03T11:08:31Z
has_accepted_license: '1'
intvolume: ' 384'
isi: 1
keyword:
- quasi curvature-dimension condition
- sub-riemannian geometry
- Sobolev-to-Lipschitz property
- Varadhan short-time asymptotics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1815-1832
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: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: Sobolev-to-Lipschitz property on QCD- spaces and applications
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 384
year: '2022'
...
---
_id: '10070'
abstract:
- lang: eng
text: We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties
for generalized intrinsic distances on strongly local Dirichlet spaces possibly
without square field operator. We present many non-smooth and infinite-dimensional
examples. As an application, we prove the integral Varadhan short-time asymptotic
with respect to a given distance function for a large class of strongly local
Dirichlet forms.
acknowledgement: 'The authors are grateful to Professor Kazuhiro Kuwae for kindly
providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful
discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They
wish to express their deepest gratitude to an anonymous Reviewer, whose punctual
remarks and comments greatly improved the accessibility and overall quality of the
initial submission. This work was completed while L.D.S. was a member of the Institut
für Angewandte Mathematik of the University of Bonn. He acknowledges funding of
his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center)
1060 - project number 211504053. He also acknowledges funding of his current position
by the Austrian Science Fund (FWF) grant F65, and by the European Research Council
(ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges
funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier
International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid
for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials
Design”, Grant Number 17H06465.'
article_number: '109234'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
2021;281(11). doi:10.1016/j.jfa.2021.109234
apa: Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2021.109234
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and
Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal
of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234.
ieee: L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces,” Journal of Functional Analysis,
vol. 281, no. 11. Elsevier, 2021.
ista: Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
281(11), 109234.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz
Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis,
vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.
short: L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).
corr_author: '1'
date_created: 2021-10-03T22:01:21Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2025-04-14T07:27:45Z
day: '15'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2021.109234
ec_funded: 1
external_id:
arxiv:
- '2008.01492'
isi:
- '000703896600005'
intvolume: ' 281'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2008.01492
month: '09'
oa: 1
oa_version: Preprint
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
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local
Dirichlet spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...