---
_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:
- access_level: open_access
checksum: 56e67756e4c6c97589a8385e15ea2d2a
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T09:38:15Z
date_updated: 2024-07-22T09:38:15Z
file_id: '17299'
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file_size: 351796
relation: main_file
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oa_version: Published Version
page: 1657-1676
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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
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file_date_updated: 2025-01-27T12:19:44Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Transactions on Machine Learning Research
publication_identifier:
issn:
- 2835-8856
publication_status: published
quality_controlled: '1'
related_material:
record:
- id: '17350'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Improved convergence of score-based diffusion models via prediction-correction
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '18899'
abstract:
- lang: eng
text: "The flourishing theory of classical optimal transport concerns mass transportation
at minimal cost. This book introduces the reader to optimal transport on quantum
structures, i.e., optimal transportation between quantum states and related non-commutative
concepts of mass transportation. It contains lecture notes on\r\n\r\nclassical
optimal transport and Wasserstein gradient flows\r\ndynamics and quantum optimal
transport\r\nquantum couplings and many-body problems\r\nquantum channels and
qubits\r\n\r\nThese notes are based on lectures given by the authors at the \"Optimal
Transport on Quantum Structures\" School held at the Erdös Center in Budapest
in the fall of 2022. The lecture notes are complemented by two survey chapters
presenting the state of the art in different research areas of non-commutative
optimal transport."
alternative_title:
- Bolyai Society Mathematical Studies
article_processing_charge: No
citation:
ama: 'Maas J, Rademacher SAE, Titkos T, Virosztek D, eds. Optimal Transport on
Quantum Structures. Vol 29. Cham: Springer Nature; 2024. doi:10.1007/978-3-031-50466-2'
apa: 'Maas, J., Rademacher, S. A. E., Titkos, T., & Virosztek, D. (Eds.). (2024).
Optimal Transport on Quantum Structures (Vol. 29). Cham: Springer Nature.
https://doi.org/10.1007/978-3-031-50466-2'
chicago: 'Maas, Jan, Simone Anna Elvira Rademacher, Tamás Titkos, and Daniel Virosztek,
eds. Optimal Transport on Quantum Structures. Vol. 29. BSMS. Cham: Springer
Nature, 2024. https://doi.org/10.1007/978-3-031-50466-2.'
ieee: 'J. Maas, S. A. E. Rademacher, T. Titkos, and D. Virosztek, Eds., Optimal
Transport on Quantum Structures, vol. 29. Cham: Springer Nature, 2024.'
ista: 'Maas J, Rademacher SAE, Titkos T, Virosztek D eds. 2024. Optimal Transport
on Quantum Structures, Cham: Springer Nature,p.'
mla: Maas, Jan, et al., editors. Optimal Transport on Quantum Structures.
Vol. 29, Springer Nature, 2024, doi:10.1007/978-3-031-50466-2.
short: J. Maas, S.A.E. Rademacher, T. Titkos, D. Virosztek, eds., Optimal Transport
on Quantum Structures, Springer Nature, Cham, 2024.
date_created: 2025-01-27T12:26:03Z
date_published: 2024-09-19T00:00:00Z
date_updated: 2025-02-17T12:22:18Z
day: '19'
department:
- _id: JaMa
doi: 10.1007/978-3-031-50466-2
editor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Simone Anna Elvira
full_name: Rademacher, Simone Anna Elvira
id: 856966FE-A408-11E9-977E-802DE6697425
last_name: Rademacher
orcid: 0000-0001-5059-4466
- first_name: Tamás
full_name: Titkos, Tamás
last_name: Titkos
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
intvolume: ' 29'
language:
- iso: eng
month: '09'
oa_version: None
place: Cham
publication_identifier:
eisbn:
- '9783031504662'
eissn:
- 2947-9460
isbn:
- '9783031504655'
issn:
- 1217-4696
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: BSMS
status: public
title: Optimal Transport on Quantum Structures
type: book_editor
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18900'
abstract:
- lang: eng
text: We prove that certain closable derivations on the GNS Hilbert space associated
with a non-tracial weight on a von Neumann algebra give rise to GNS-symmetric
semigroups of contractive completely positive maps on the von Neumann algebra.
acknowledgement: 'The author was funded by the Austrian Science Fund 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 version arising
from this submission. '
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. Modular completely Dirichlet forms as squares of derivations. International
Mathematics Research Notices. 2024;2024(14):10597-10614. doi:10.1093/imrn/rnae092
apa: Wirth, M. (2024). Modular completely Dirichlet forms as squares of derivations.
International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae092
chicago: Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.”
International Mathematics Research Notices. Oxford University Press, 2024.
https://doi.org/10.1093/imrn/rnae092.
ieee: M. Wirth, “Modular completely Dirichlet forms as squares of derivations,”
International Mathematics Research Notices, vol. 2024, no. 14. Oxford University
Press, pp. 10597–10614, 2024.
ista: Wirth M. 2024. Modular completely Dirichlet forms as squares of derivations.
International Mathematics Research Notices. 2024(14), 10597–10614.
mla: Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.”
International Mathematics Research Notices, vol. 2024, no. 14, Oxford University
Press, 2024, pp. 10597–614, doi:10.1093/imrn/rnae092.
short: M. Wirth, International Mathematics Research Notices 2024 (2024) 10597–10614.
corr_author: '1'
date_created: 2025-01-27T12:36:10Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-09T12:02:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1093/imrn/rnae092
external_id:
isi:
- '001222279400001'
file:
- access_level: open_access
checksum: 3e1f80d58ada0c60a58f35df8080967e
content_type: application/pdf
creator: dernst
date_created: 2025-01-27T12:38:10Z
date_updated: 2025-01-27T12:38:10Z
file_id: '18901'
file_name: 2024_IMRN_Wirth.pdf
file_size: 689984
relation: main_file
success: 1
file_date_updated: 2025-01-27T12:38:10Z
has_accepted_license: '1'
intvolume: ' 2024'
isi: 1
issue: '14'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 10597-10614
project:
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modular completely Dirichlet forms as squares of derivations
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: 2024
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14934'
abstract:
- lang: eng
text: "We study random perturbations of a Riemannian manifold (M, g) by means of
so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the
given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the
conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular
case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated
Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric
and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion,
spectral bound, or spectral gap change under the influence of the noise. And if
so, is\r\nit possible to quantify these dependencies in terms of key parameters
of the noise? Another\r\ngoal is to define and analyze in detail the Fractional
Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent
interest."
acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for
valuable discussions on this project. They are also grateful to Nathanaël Berestycki,
and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24],
and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous
version of the proof of Proposition 3.10. The authors feel very much indebted to
an anonymous reviewer for his/her careful reading and the many valuable suggestions
that have significantly contributed to the improvement of the paper. L.D.S. gratefully
acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC
1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65
at Institute of Science and Technology Austria. This research was funded in whole
or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open
access, the authors have applied a CC BY public copyright licence to any Author
Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff
Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian
geometry. Potential Analysis. 2024;61:501-553. doi:10.1007/s11118-023-10118-0
apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour
in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0
chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery
Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature,
2024. https://doi.org/10.1007/s11118-023-10118-0.
ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random
Riemannian geometry,” Potential Analysis, vol. 61. Springer Nature, pp.
501–553, 2024.
ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian
geometry. Potential Analysis. 61, 501–553.
mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.”
Potential Analysis, vol. 61, Springer Nature, 2024, pp. 501–53, doi:10.1007/s11118-023-10118-0.
short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis 61 (2024) 501–553.
date_created: 2024-02-04T23:00:54Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T11:57:14Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-023-10118-0
external_id:
arxiv:
- '2012.06796'
isi:
- '001151118800001'
file:
- access_level: open_access
checksum: 33c688bdf296c3d8f8bbd96c7dd26037
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:13:34Z
date_updated: 2025-01-09T08:13:34Z
file_id: '18789'
file_name: 2024_PotentialAnalysis_DelloSchiavo.pdf
file_size: 1294993
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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: '15350'
abstract:
- lang: eng
text: We extend three related results from the analysis of influences of Boolean
functions to the quantum setting, namely the KKL theorem, Friedgut’s Junta theorem
and Talagrand’s variance inequality for geometric influences. Our results are
derived by a joint use of recently studied hypercontractivity and gradient estimates.
These generic tools also allow us to derive generalizations of these results in
a general von Neumann algebraic setting beyond the case of the quantum hypercube,
including examples in infinite dimensions relevant to quantum information theory
such as continuous variables quantum systems. Finally, we comment on the implications
of our results as regards to noncommutative extensions of isoperimetric type inequalities,
quantum circuit complexity lower bounds and the learnability of quantum observables.
acknowledgement: "Open access funding provided by the Carolinas Consortium.\r\nH.Z.
is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.
H.Z. would like to thank the American Institute of Mathematics and the AIM workshop
Analysis on the hypercube with applications to quantum computing. He is also grateful
to the organizers and other participants for creating an active atmosphere. The
research of C.R. has been supported by ANR project QTraj (ANR-20-CE40-0024-01) of
the French National Research Agency (ANR). C.R. acknowledges the support of the
Munich Center for Quantum Sciences and Technology, as well as the Humboldt Foundation.
C.R. would like to thank Amanda Young for fruitful discussion on the applications
of Friedgut’s Junta theorem to learning quantum dynamics. The research of 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.
The authors want to thank Francisco Escudero Gutierrez and Hsin-Yuan Huang for helpful
comments on an earlier version of the paper. They are grateful to the referees for
the careful reading and helpful comments."
article_number: '95'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Cambyse
full_name: Rouzé, Cambyse
last_name: Rouzé
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Rouzé C, Wirth M, Zhang H. Quantum Talagrand, KKL and Friedgut’s theorems and
the learnability of quantum boolean functions. Communications in Mathematical
Physics. 2024;405(4). doi:10.1007/s00220-024-04981-0
apa: Rouzé, C., Wirth, M., & Zhang, H. (2024). Quantum Talagrand, KKL and Friedgut’s
theorems and the learnability of quantum boolean functions. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-024-04981-0
chicago: Rouzé, Cambyse, Melchior Wirth, and Haonan Zhang. “Quantum Talagrand, KKL
and Friedgut’s Theorems and the Learnability of Quantum Boolean Functions.” Communications
in Mathematical Physics. Springer Nature, 2024. https://doi.org/10.1007/s00220-024-04981-0.
ieee: C. Rouzé, M. Wirth, and H. Zhang, “Quantum Talagrand, KKL and Friedgut’s theorems
and the learnability of quantum boolean functions,” Communications in Mathematical
Physics, vol. 405, no. 4. Springer Nature, 2024.
ista: Rouzé C, Wirth M, Zhang H. 2024. Quantum Talagrand, KKL and Friedgut’s theorems
and the learnability of quantum boolean functions. Communications in Mathematical
Physics. 405(4), 95.
mla: Rouzé, Cambyse, et al. “Quantum Talagrand, KKL and Friedgut’s Theorems and
the Learnability of Quantum Boolean Functions.” Communications in Mathematical
Physics, vol. 405, no. 4, 95, Springer Nature, 2024, doi:10.1007/s00220-024-04981-0.
short: C. Rouzé, M. Wirth, H. Zhang, Communications in Mathematical Physics 405
(2024).
corr_author: '1'
date_created: 2024-04-29T08:47:28Z
date_published: 2024-04-09T00:00:00Z
date_updated: 2025-09-04T13:50:22Z
day: '09'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00220-024-04981-0
external_id:
arxiv:
- '2209.07279'
isi:
- '001199509500004'
pmid:
- '38606337'
file:
- access_level: open_access
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creator: dernst
date_created: 2024-05-06T06:18:45Z
date_updated: 2024-05-06T06:18:45Z
file_id: '15365'
file_name: 2024_CommMathPhysics_Rouze.pdf
file_size: 653676
relation: main_file
success: 1
file_date_updated: 2024-05-06T06:18:45Z
has_accepted_license: '1'
intvolume: ' 405'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
- _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: Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum
boolean functions
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: 405
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15373'
abstract:
- lang: eng
text: In this article we prove a refined version of the Christensen–Evans theorem
for generators of uniformly continuous GNS-symmetric quantum Markov semigroups.
We use this result to show the existence of GNS-symmetric extensions of GNS-symmetric
quantum Markov semigroups. In particular, this implies that the generators of
GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra
can be written in the form specified by Alicki's theorem.
article_number: '110475'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. Christensen–Evans theorem and extensions of GNS-symmetric quantum
Markov semigroups. Journal of Functional Analysis. 2024;287(3). doi:10.1016/j.jfa.2024.110475
apa: Wirth, M. (2024). Christensen–Evans theorem and extensions of GNS-symmetric
quantum Markov semigroups. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110475
chicago: Wirth, Melchior. “Christensen–Evans Theorem and Extensions of GNS-Symmetric
Quantum Markov Semigroups.” Journal of Functional Analysis. Elsevier, 2024.
https://doi.org/10.1016/j.jfa.2024.110475.
ieee: M. Wirth, “Christensen–Evans theorem and extensions of GNS-symmetric quantum
Markov semigroups,” Journal of Functional Analysis, vol. 287, no. 3. Elsevier,
2024.
ista: Wirth M. 2024. Christensen–Evans theorem and extensions of GNS-symmetric quantum
Markov semigroups. Journal of Functional Analysis. 287(3), 110475.
mla: Wirth, Melchior. “Christensen–Evans Theorem and Extensions of GNS-Symmetric
Quantum Markov Semigroups.” Journal of Functional Analysis, vol. 287, no.
3, 110475, Elsevier, 2024, doi:10.1016/j.jfa.2024.110475.
short: M. Wirth, Journal of Functional Analysis 287 (2024).
corr_author: '1'
date_created: 2024-05-12T22:01:01Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T07:24:07Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2024.110475
external_id:
isi:
- '001237916800001'
file:
- access_level: open_access
checksum: 657c9f77dd30bb31ce43a591f58126a2
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T09:33:56Z
date_updated: 2025-01-09T09:33:56Z
file_id: '18802'
file_name: 2024_JourFunctAnalysis_Wirth.pdf
file_size: 503148
relation: main_file
success: 1
file_date_updated: 2025-01-09T09:33:56Z
has_accepted_license: '1'
intvolume: ' 287'
isi: 1
issue: '3'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
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: Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups
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: 287
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '17277'
abstract:
- lang: eng
text: "This paper is devoted to stability results for the Gaussian logarithmic Sobolev
inequality, with explicit stability constants.\r\n\r\n"
acknowledgement: The authors thank Max Fathi and Pierre Cardaliaguet for fruitful
discussions and Emanuel Indrei for stimulating interactions. They also thank an
anonymous referee for useful comments and suggestions which have led to an improvement
of the manuscript. They also want to express their gratitude to the managing editor,
L. Gross, for his encouragements and questions. G.B. has been funded by the European
Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie
grant agreement No 754362. This work has been (partially) supported by the Project
Conviviality ANR-23-CE40-0003 of the French National Research Agency.
article_number: '110562'
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: 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. Stability for the logarithmic Sobolev inequality.
Journal of Functional Analysis. 2024;287(8). doi:10.1016/j.jfa.2024.110562
apa: Brigati, G., Dolbeault, J., & Simonov, N. (2024). Stability for the logarithmic
Sobolev inequality. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110562
chicago: Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. “Stability for the
Logarithmic Sobolev Inequality.” Journal of Functional Analysis. Elsevier,
2024. https://doi.org/10.1016/j.jfa.2024.110562.
ieee: G. Brigati, J. Dolbeault, and N. Simonov, “Stability for the logarithmic Sobolev
inequality,” Journal of Functional Analysis, vol. 287, no. 8. Elsevier,
2024.
ista: Brigati G, Dolbeault J, Simonov N. 2024. Stability for the logarithmic Sobolev
inequality. Journal of Functional Analysis. 287(8), 110562.
mla: Brigati, Giovanni, et al. “Stability for the Logarithmic Sobolev Inequality.”
Journal of Functional Analysis, vol. 287, no. 8, 110562, Elsevier, 2024,
doi:10.1016/j.jfa.2024.110562.
short: G. Brigati, J. Dolbeault, N. Simonov, Journal of Functional Analysis 287
(2024).
corr_author: '1'
date_created: 2024-07-21T22:01:00Z
date_published: 2024-10-15T00:00:00Z
date_updated: 2025-09-08T08:25:34Z
day: '15'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2024.110562
external_id:
arxiv:
- '2303.12926'
isi:
- '001271814000001'
intvolume: ' 287'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 10.48550/arXiv.2303.12926
month: '10'
oa: 1
oa_version: Preprint
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: Stability for the logarithmic Sobolev inequality
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 287
year: '2024'
...
---
_id: '17282'
abstract:
- lang: eng
text: Let X be a vector field and Y be a co-vector field on a smooth manifold M.
Does there exist a smooth Riemannian metric gαβ on M such that Yβ=gαβXα ?
The main result of this note gives necessary and sufficient conditions for this
to be true. As an application of this result we show that a finite-dimensional
ergodic Lindblad equation admits a gradient flow structure for the von Neumann
relative entropy if and only if the condition of BKM-detailed balance holds.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).J. M. gratefully acknowledges support by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB
F65. We thank the anonymous referee for valuable comments on the paper.
article_number: '153'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Morris
full_name: Brooks, Morris
id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
last_name: Brooks
orcid: 0000-0002-6249-0928
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Brooks M, Maas J. Characterisation of gradient flows for a given functional.
Calculus of Variations and Partial Differential Equations. 2024;63(6).
doi:10.1007/s00526-024-02755-z
apa: Brooks, M., & Maas, J. (2024). Characterisation of gradient flows for a
given functional. Calculus of Variations and Partial Differential Equations.
Springer Nature. https://doi.org/10.1007/s00526-024-02755-z
chicago: Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a
given Functional.” Calculus of Variations and Partial Differential Equations.
Springer Nature, 2024. https://doi.org/10.1007/s00526-024-02755-z.
ieee: M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,”
Calculus of Variations and Partial Differential Equations, vol. 63, no.
6. Springer Nature, 2024.
ista: Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional.
Calculus of Variations and Partial Differential Equations. 63(6), 153.
mla: Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given
Functional.” Calculus of Variations and Partial Differential Equations,
vol. 63, no. 6, 153, Springer Nature, 2024, doi:10.1007/s00526-024-02755-z.
short: M. Brooks, J. Maas, Calculus of Variations and Partial Differential Equations
63 (2024).
corr_author: '1'
date_created: 2024-07-21T22:01:01Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:24:51Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-024-02755-z
ec_funded: 1
external_id:
arxiv:
- '2209.11149'
isi:
- '001258097800003'
pmid:
- '38947856'
file:
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checksum: a0cf0e0ba2157aabb287cb597be17dac
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month: '07'
oa: 1
oa_version: Published Version
pmid: 1
project:
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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: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
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issn:
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publisher: Springer Nature
quality_controlled: '1'
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status: public
title: Characterisation of gradient flows for a given functional
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
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abstract:
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text: "This thesis deals with the study of stochastic processes and their ergodicity
properties. The\r\nvariety of problems encountered calls for a set of different
approaches, ranging from classical to\r\nmodern ones: a special place is held
by probabilistic methods based on couplings, by functional\r\ninequalities, and
by the theory of gradient flows in the space of measures.\r\n\r\nThe material
is organized as follows. Chapter 1 contains the introduction to this thesis, starting\r\nwith
a general presentation of some of the relevant topics. Section 1.1 is dedicated
to the\r\ntheory of gradient flows in metric spaces, and introduces the first
contribution of this thesis\r\n[DSMP24], which is presented in detail in Chapter
2. Section 1.2 moves to the topic of\r\ncurvature of Markov chains, concluding
with a brief description of our second contribution\r\n[Ped23], which is included
in Chapter 3. Section 1.3 discusses applications of stochastic\r\nprocesses to
the theory of sampling, in particular the recent framework of score-based diffusion\r\nmodels,
and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses\r\nsome
related problems, concerning the regularization properties of the heat flow. It
serves\r\nas a motivation for the work [BP24], which we report in Chapter 5. Finally,
Section 1.5\r\ndiscusses the last contribution of this thesis, which can be found
in Chapter 6. It deals with\r\nthe convergence to equilibrium of a particular
stochastic model from quantitative genetics:\r\nthis is established via some functional
inequalities, which we prove with probabilistic arguments\r\nbased on couplings.\r\n"
alternative_title:
- ISTA Thesis
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author:
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full_name: Pedrotti, Francesco
id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
last_name: Pedrotti
citation:
ama: Pedrotti F. Functional inequalities and convergence of stochastic processes.
2024. doi:10.15479/at:ista:17336
apa: Pedrotti, F. (2024). Functional inequalities and convergence of stochastic
processes. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17336
chicago: Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic
Processes.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17336.
ieee: F. Pedrotti, “Functional inequalities and convergence of stochastic processes,”
Institute of Science and Technology Austria, 2024.
ista: Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes.
Institute of Science and Technology Austria.
mla: Pedrotti, Francesco. Functional Inequalities and Convergence of Stochastic
Processes. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17336.
short: F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes,
Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-07-29T09:14:14Z
date_published: 2024-07-31T00:00:00Z
date_updated: 2026-04-07T13:00:03Z
day: '31'
ddc:
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- _id: JaMa
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month: '07'
oa: 1
oa_version: Published Version
page: '183'
project:
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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_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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- id: '17352'
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status: public
- id: '17143'
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: Functional inequalities and convergence of stochastic processes
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legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
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
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Transactions of the American Mathematical Society
publication_identifier:
eissn:
- 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: repository
_id: '17350'
abstract:
- lang: eng
text: "Score-based generative models (SGMs) are powerful tools to sample from\r\ncomplex
data distributions. Their underlying idea is to (i) run a forward\r\nprocess for
time $T_1$ by adding noise to the data, (ii) estimate its score\r\nfunction, and
(iii) use such estimate to run a reverse process. As the reverse\r\nprocess is
initialized with the stationary distribution of the forward one, the\r\nexisting
analysis paradigm requires $T_1\\to\\infty$. This is however\r\nproblematic: from
a theoretical viewpoint, for a given precision of the score\r\napproximation,
the convergence guarantee fails as $T_1$ diverges; from a\r\npractical viewpoint,
a large $T_1$ increases computational costs and leads to\r\nerror propagation.
This paper addresses the issue by considering a version of\r\nthe popular predictor-corrector
scheme: after running the forward process, we\r\nfirst estimate the final distribution
via an inexact Langevin dynamics and then\r\nrevert the process. Our key technical
contribution is to provide convergence\r\nguarantees which require to run the
forward process only for a fixed finite\r\ntime $T_1$. Our bounds exhibit a mild
logarithmic dependence on the input\r\ndimension and the subgaussian norm of the
target distribution, have minimal\r\nassumptions on the data, and require only
to control the $L^2$ loss on the\r\nscore approximation, which is the quantity
minimized in practice."
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. arXiv. doi:10.48550/arXiv.2305.14164
apa: Pedrotti, F., Maas, J., & Mondelli, M. (n.d.). Improved convergence of
score-based diffusion models via prediction-correction. arXiv. https://doi.org/10.48550/arXiv.2305.14164
chicago: Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence
of Score-Based Diffusion Models via Prediction-Correction.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.2305.14164.
ieee: F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based
diffusion models via prediction-correction,” arXiv. .
ista: Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion
models via prediction-correction. arXiv, 10.48550/arXiv.2305.14164.
mla: Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion
Models via Prediction-Correction.” ArXiv, doi:10.48550/arXiv.2305.14164.
short: F. Pedrotti, J. Maas, M. Mondelli, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-07-31T07:56:40Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2026-04-07T13:00:02Z
day: '06'
department:
- _id: JaMa
- _id: MaMo
doi: 10.48550/arXiv.2305.14164
external_id:
arxiv:
- '2305.14164'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2305.14164
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18897'
relation: later_version
status: public
- id: '17336'
relation: dissertation_contains
status: public
status: public
title: Improved convergence of score-based diffusion models via prediction-correction
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
_id: '17352'
abstract:
- lang: eng
text: "We prove upper bounds on the $L^\\infty$-Wasserstein distance from optimal\r\ntransport
between strongly log-concave probability densities and log-Lipschitz\r\nperturbations.
In the simplest setting, such a bound amounts to a\r\ntransport-information inequality
involving the $L^\\infty$-Wasserstein metric\r\nand the relative $L^\\infty$-Fisher
information. We show that this inequality\r\ncan be sharpened significantly in
situations where the involved densities are\r\nanisotropic. Our proof is based
on probabilistic techniques using Langevin\r\ndynamics. As an application of these
results, we obtain sharp exponential rates\r\nof convergence in Fisher's infinitesimal
model from quantitative genetics,\r\ngeneralising recent results by Calvez, Poyato,
and Santambrogio in dimension 1\r\nto arbitrary dimensions."
article_number: '2402.04151'
article_processing_charge: No
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. arXiv.
doi:10.48550/arXiv.2402.04151
apa: Khudiakova, K., Maas, J., & Pedrotti, F. (n.d.). L∞-optimal transport of
anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal
model. arXiv. https://doi.org/10.48550/arXiv.2402.04151
chicago: Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport
of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal
Model.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2402.04151.
ieee: K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic
log-concave measures and exponential convergence in Fisher’s infinitesimal model,”
arXiv. .
ista: Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave
measures and exponential convergence in Fisher’s infinitesimal model. arXiv, 2402.04151.
mla: Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave
Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” ArXiv,
2402.04151, doi:10.48550/arXiv.2402.04151.
short: K. Khudiakova, J. Maas, F. Pedrotti, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-07-31T08:07:40Z
date_published: 2024-02-07T00:00:00Z
date_updated: 2026-04-07T13:00:02Z
day: '07'
department:
- _id: JaMa
doi: 10.48550/arXiv.2402.04151
external_id:
arxiv:
- '2402.04151'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2402.04151
month: '02'
oa: 1
oa_version: Preprint
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: arXiv
publication_status: draft
related_material:
record:
- id: '20050'
relation: later_version
status: public
- id: '17336'
relation: dissertation_contains
status: public
status: public
title: L∞-optimal transport of anisotropic log-concave measures and exponential convergence
in Fisher's infinitesimal model
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
_id: '17353'
abstract:
- lang: eng
text: "In this paper we derive estimates for the Hessian of the logarithm\r\n(log-Hessian)
for solutions to the heat equation. For initial data in the form\r\nof log-Lipschitz
perturbation of strongly log-concave measures, the log-Hessian\r\nadmits an explicit,
uniform (in space) lower bound. This yields a new estimate\r\nfor the Lipschitz
constant of a transport map pushing forward the standard\r\nGaussian to a measure
in this class. Further connections are discussed with\r\nscore-based diffusion
models and improved Gaussian logarithmic Sobolev\r\ninequalities. Finally, we
show that assuming only fast decay of the tails of\r\nthe initial datum does not
suffice to guarantee uniform log-Hessian upper\r\nbounds."
article_number: '2404.15205'
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: 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.
arXiv. doi:10.48550/arXiv.2404.15205
apa: Brigati, G., & Pedrotti, F. (n.d.). Heat flow, log-concavity, and Lipschitz
transport maps. arXiv. https://doi.org/10.48550/arXiv.2404.15205
chicago: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and
Lipschitz Transport Maps.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2404.15205.
ieee: G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport
maps,” arXiv. .
ista: Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps.
arXiv, 2404.15205.
mla: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz
Transport Maps.” ArXiv, 2404.15205, doi:10.48550/arXiv.2404.15205.
short: G. Brigati, F. Pedrotti, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-07-31T08:17:14Z
date_published: 2024-05-08T00:00:00Z
date_updated: 2026-04-07T13:00:02Z
day: '08'
department:
- _id: JaMa
doi: 10.48550/arXiv.2404.15205
external_id:
arxiv:
- '2404.15205'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2404.15205
month: '05'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20591'
relation: later_version
status: public
- id: '17336'
relation: dissertation_contains
status: public
status: public
title: Heat flow, log-concavity, and Lipschitz transport maps
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_type: green
_id: '21967'
abstract:
- lang: eng
text: "Selection against deleterious mutations, called purifying selection, plays
a central role in evolution and acts in all populations. It is known that the
genetic patterns observed in genomic regions undergoing purifying selection differ
from those resulting from neutral evolution. However, a comprehensive understanding
of the underlying mechanisms shaping those patterns is still lacking.\r\n\r\nIn
the present work, we use simulations combined with a genealogical approach to
identify the effect of purifying selection on the ancestry and thus on the genetic
diversity. Our analysis relies on the postulate that the genealogy belongs to
the universality class of Beta-coalescents. Under this assumption, we derive statistics
measuring the distortion of the genealogy. This approach allows us to consider
a wide range of regimes (i.e. arbitrary selection and mutation strengths) and
uncover a rich phase diagram. We find that, for strong selection, the limiting
genealogy is given by Kingman’s coalescent on a polynomial timescale. As selection
gets weaker, Muller’s ratchet starts operating, setting off the emergence of multiple
mergers in the genealogical structures. Our results show that while multiple-merger
coalescents are often interpreted as the signature of selective sweeps in rapidly
adapting populations, these structures can also appear in the context of Muller’s
ratchet."
acknowledgement: This work was supported by the Austrian Academy of Science, DOC fellowship
No 26293 (K.K.) and the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie grant agreement No 101034413 (J.T.). Simulations
were performed on the ISTA High-performance Computing Cluster.
article_processing_charge: No
author:
- first_name: Kseniia
full_name: Khudiakova, Kseniia
id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
last_name: Khudiakova
orcid: 0000-0002-6246-1465
- first_name: Florin
full_name: Boenkost, Florin
last_name: Boenkost
- first_name: Julie N
full_name: Tourniaire, Julie N
id: 5dc06dd8-8e51-11ec-9170-8d9c450cc216
last_name: Tourniaire
citation:
ama: Khudiakova K, Boenkost F, Tourniaire JN. Genealogies under purifying selection.
bioRxiv. doi:10.1101/2024.10.15.618444
apa: Khudiakova, K., Boenkost, F., & Tourniaire, J. N. (n.d.). Genealogies under
purifying selection. bioRxiv. https://doi.org/10.1101/2024.10.15.618444
chicago: Khudiakova, Kseniia, Florin Boenkost, and Julie N Tourniaire. “Genealogies
under Purifying Selection.” BioRxiv, n.d. https://doi.org/10.1101/2024.10.15.618444.
ieee: K. Khudiakova, F. Boenkost, and J. N. Tourniaire, “Genealogies under purifying
selection,” bioRxiv. .
ista: Khudiakova K, Boenkost F, Tourniaire JN. Genealogies under purifying selection.
bioRxiv, 10.1101/2024.10.15.618444.
mla: Khudiakova, Kseniia, et al. “Genealogies under Purifying Selection.” BioRxiv,
doi:10.1101/2024.10.15.618444.
short: K. Khudiakova, F. Boenkost, J.N. Tourniaire, BioRxiv (n.d.).
corr_author: '1'
date_created: 2026-06-09T12:14:08Z
date_published: 2024-10-18T00:00:00Z
date_updated: 2026-06-12T12:43:34Z
day: '18'
department:
- _id: NiBa
- _id: JaMa
doi: 10.1101/2024.10.15.618444
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1101/2024.10.15.618444
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8
grant_number: '26293'
name: The impact of deleterious mutations on small populations
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: bioRxiv
publication_status: draft
related_material:
record:
- id: '21918'
relation: dissertation_contains
status: public
status: public
title: Genealogies under purifying selection
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18706'
abstract:
- lang: eng
text: "We prove discrete-to-continuum convergence for dynamical optimal transport
on Zd\r\n -periodic graphs with cost functional having linear growth at infinity.
This result provides an answer to a problem left open by Gladbach, Kopfer, Maas,
and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the
convergence behaviour of discrete boundary-value dynamical transport problems
is proved under the stronger assumption of superlinear growth. Our result extends
the known literature to some important classes of examples, such as scaling limits
of 1 -Wasserstein transport problems. Similarly to what happens in the quadratic
case, the geometry of the graph plays a crucial role in the structure of the limit
cost function, as we discuss in the final part of this work, which includes some
visual representations."
acknowledgement: L.P. gratefully acknowledges fundings from the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1,
Projekt-ID 390685813. F.Q. gratefully acknowledges support from the Austrian Science
Fund (FWF) project 10.55776/F65.
article_processing_charge: Yes
article_type: original
author:
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Portinale L, Quattrocchi F. Discrete-to-continuum limits of optimal transport
with linear growth on periodic graphs. European Journal of Applied Mathematics.
2024:1-29. doi:10.1017/s0956792524000810
apa: Portinale, L., & Quattrocchi, F. (2024). Discrete-to-continuum limits of
optimal transport with linear growth on periodic graphs. European Journal of
Applied Mathematics. Cambridge University Press. https://doi.org/10.1017/s0956792524000810
chicago: Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits
of Optimal Transport with Linear Growth on Periodic Graphs.” European Journal
of Applied Mathematics. Cambridge University Press, 2024. https://doi.org/10.1017/s0956792524000810.
ieee: L. Portinale and F. Quattrocchi, “Discrete-to-continuum limits of optimal
transport with linear growth on periodic graphs,” European Journal of Applied
Mathematics. Cambridge University Press, pp. 1–29, 2024.
ista: Portinale L, Quattrocchi F. 2024. Discrete-to-continuum limits of optimal
transport with linear growth on periodic graphs. European Journal of Applied Mathematics.,
1–29.
mla: Portinale, Lorenzo, and Filippo Quattrocchi. “Discrete-to-Continuum Limits
of Optimal Transport with Linear Growth on Periodic Graphs.” European Journal
of Applied Mathematics, Cambridge University Press, 2024, pp. 1–29, doi:10.1017/s0956792524000810.
short: L. Portinale, F. Quattrocchi, European Journal of Applied Mathematics (2024)
1–29.
date_created: 2024-12-23T11:03:59Z
date_published: 2024-12-20T00:00:00Z
date_updated: 2026-06-19T22:31:23Z
day: '20'
ddc:
- '500'
department:
- _id: GradSch
- _id: JaMa
doi: 10.1017/s0956792524000810
external_id:
isi:
- '001381435800001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1017/S0956792524000810
month: '12'
oa: 1
oa_version: Published Version
page: 1-29
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: European Journal of Applied Mathematics
publication_identifier:
eissn:
- 1469-4425
issn:
- 0956-7925
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '20563'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Discrete-to-continuum limits of optimal transport with linear growth on periodic
graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20571'
abstract:
- lang: eng
text: "We prove the convergence of a modified Jordan--Kinderlehrer--Otto scheme
to a solution to the Fokker--Planck equation in $\\Omega \\Subset \\mathbb{R}^d$
with general, positive and temporally constant, Dirichlet boundary conditions.
We work under mild assumptions on the domain, the drift, and the initial datum.
\ In the special case where $\\Omega$ is an interval in $\\mathbb{R}^1$, we prove
that such a solution is a gradient flow -- curve of maximal slope -- within a
suitable space of measures, endowed with a modified Wasserstein distance.\r\nOur
discrete scheme and modified distance draw inspiration from contributions by A.
Figalli and N. Gigli [J. Math. Pures Appl. 94, (2010), pp. 107--130], and J. Morales
[J. Math. Pures Appl. 112, (2018), pp. 41--88] on an optimal-transport approach
to evolution equations with Dirichlet boundary conditions. Similarly to these
works, we allow the mass to flow from/to the boundary $\\partial \\Omega$ throughout
the evolution. However, our leading idea is to also keep track of the mass at
the boundary by working with measures defined on the whole closure $\\overline
\\Omega$. The driving functional is a modification of the classical relative entropy
that also makes use of the information at the boundary. As an intermediate result,
when $\\Omega$ is an interval in $\\mathbb{R}^1$, we find a formula for the descending
slope of this geodesically nonconvex functional. "
acknowledgement: "The author would like to thank Jan Maas for suggesting this project
and for many helpful\r\ncomments, Antonio Agresti, Lorenzo Dello Schiavo and Julian
Fischer for several fruitful discussions, and Oliver Tse for pointing out the reference
[15]. He also gratefully acknowledges support from the Austrian Science Fund (FWF)
project 10.55776/F65.\r\n"
article_number: '2403.07803'
article_processing_charge: No
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. arXiv. doi:10.48550/arXiv.2403.07803
apa: Quattrocchi, F. (n.d.). Variational structures for the Fokker-Planck equation
with general Dirichlet boundary conditions. arXiv. https://doi.org/10.48550/arXiv.2403.07803
chicago: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2403.07803.
ieee: F. Quattrocchi, “Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions,” arXiv. .
ista: Quattrocchi F. Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions. arXiv, 2403.07803.
mla: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” ArXiv, 2403.07803, doi:10.48550/arXiv.2403.07803.
short: F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:56Z
date_published: 2024-04-09T00:00:00Z
date_updated: 2026-06-19T22:31:23Z
day: '09'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2403.07803
external_id:
arxiv:
- '2403.07803'
keyword:
- gradient flows
- Jordan–Kinderlehrer–Otto scheme
- curves of maximal slope
- optimal transport
- Dirichlet boundary conditions
- Fokker–Planck equation
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2403.07803
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20865'
relation: later_version
status: public
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: Variational structures for the Fokker-Planck equation with general Dirichlet
boundary conditions
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...