---
_id: '12216'
abstract:
- lang: eng
text: Many trace inequalities can be expressed either as concavity/convexity theorems
or as monotonicity theorems. A classic example is the joint convexity of the quantum
relative entropy which is equivalent to the Data Processing Inequality. The latter
says that quantum operations can never increase the relative entropy. The monotonicity
versions often have many advantages, and often have direct physical application,
as in the example just mentioned. Moreover, the monotonicity results are often
valid for a larger class of maps than, say, quantum operations (which are completely
positive). In this paper we prove several new monotonicity results, the first
of which is a monotonicity theorem that has as a simple corollary a celebrated
concavity theorem of Epstein. Our starting points are the monotonicity versions
of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs
of these in their general forms using interpolation. We then prove our new monotonicity
theorems by several duality arguments.
acknowledgement: Work partially supported by the Lise Meitner fellowship, Austrian
Science Fund (FWF) M3337.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Eric A.
full_name: Carlen, Eric A.
last_name: Carlen
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and
related inequalities. Linear Algebra and its Applications. 2022;654:289-310.
doi:10.1016/j.laa.2022.09.001
apa: Carlen, E. A., & Zhang, H. (2022). Monotonicity versions of Epstein’s concavity
theorem and related inequalities. Linear Algebra and Its Applications.
Elsevier. https://doi.org/10.1016/j.laa.2022.09.001
chicago: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s
Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications.
Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001.
ieee: E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem
and related inequalities,” Linear Algebra and its Applications, vol. 654.
Elsevier, pp. 289–310, 2022.
ista: Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem
and related inequalities. Linear Algebra and its Applications. 654, 289–310.
mla: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity
Theorem and Related Inequalities.” Linear Algebra and Its Applications,
vol. 654, Elsevier, 2022, pp. 289–310, doi:10.1016/j.laa.2022.09.001.
short: E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.
date_created: 2023-01-16T09:46:38Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-04T09:24:51Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1016/j.laa.2022.09.001
external_id:
isi:
- '000860689600014'
file:
- access_level: open_access
checksum: cf3cb7e7e34baa967849f01d8f0c1ae4
content_type: application/pdf
creator: dernst
date_created: 2023-01-27T08:08:39Z
date_updated: 2023-01-27T08:08:39Z
file_id: '12415'
file_name: 2022_LinearAlgebra_Carlen.pdf
file_size: 441184
relation: main_file
success: 1
file_date_updated: 2023-01-27T08:08:39Z
has_accepted_license: '1'
intvolume: ' 654'
isi: 1
keyword:
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Numerical Analysis
- Algebra and Number Theory
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 289-310
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Monotonicity versions of Epstein's concavity theorem and related 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 654
year: '2022'
...
---
_id: '12281'
abstract:
- lang: eng
text: We study the hydrodynamic and hydrostatic limits of the one-dimensional open
symmetric inclusion process with slow boundary. Depending on the value of the
parameter tuning the interaction rate of the bulk of the system with the boundary,
we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary
conditions as hydrodynamic equation. In our approach, we combine duality and first-second
class particle techniques to reduce the scaling limit of the inclusion process
to the limiting behavior of a single, non-interacting, particle.
acknowledgement: "C.F. and P.G. thank FCT/Portugal for support through the project
UID/MAT/04459/2013.\r\nThis project has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovative programme
(grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020
research and innovation programme under the Marie-Skłodowska-Curie grant agreement
No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at
an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this
work has been done, and the European research and innovative programme No. 715734
for the kind hospitality."
article_processing_charge: No
article_type: original
author:
- first_name: Chiara
full_name: Franceschini, Chiara
last_name: Franceschini
- first_name: Patrícia
full_name: Gonçalves, Patrícia
last_name: Gonçalves
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: 'Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow
boundary: Hydrodynamics and hydrostatics. Bernoulli. 2022;28(2):1340-1381.
doi:10.3150/21-bej1390'
apa: 'Franceschini, C., Gonçalves, P., & Sau, F. (2022). Symmetric inclusion
process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli.
Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/21-bej1390'
chicago: 'Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric
Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli.
Bernoulli Society for Mathematical Statistics and Probability, 2022. https://doi.org/10.3150/21-bej1390.'
ieee: 'C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with
slow boundary: Hydrodynamics and hydrostatics,” Bernoulli, vol. 28, no.
2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381,
2022.'
ista: 'Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with
slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.'
mla: 'Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary:
Hydrodynamics and Hydrostatics.” Bernoulli, vol. 28, no. 2, Bernoulli Society
for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:10.3150/21-bej1390.'
short: C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381.
date_created: 2023-01-16T10:03:04Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2023-08-04T10:27:35Z
day: '01'
department:
- _id: JaMa
doi: 10.3150/21-bej1390
ec_funded: 1
external_id:
arxiv:
- '2007.11998'
isi:
- '000766619100025'
intvolume: ' 28'
isi: 1
issue: '2'
keyword:
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2007.11998
month: '05'
oa: 1
oa_version: Preprint
page: 1340-1381
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Bernoulli
publication_identifier:
issn:
- 1350-7265
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 28
year: '2022'
...
---
_id: '10797'
abstract:
- lang: eng
text: We consider symmetric partial exclusion and inclusion processes in a general
graph in contact with reservoirs, where we allow both for edge disorder and well-chosen
site disorder. We extend the classical dualities to this context and then we derive
new orthogonal polynomial dualities. From the classical dualities, we derive the
uniqueness of the non-equilibrium steady state and obtain correlation inequalities.
Starting from the orthogonal polynomial dualities, we show universal properties
of n-point correlation functions in the non-equilibrium steady state for systems
with at most two different reservoir parameters, such as a chain with reservoirs
at left and right ends.
- lang: fre
text: Nous considérons des processus d’exclusion partielle, et des processus d’inclusion
sur un graphe général en contact avec des réservoirs. Nous autorisons la présence
de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons
les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités
orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état
stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir
des dualités orthogonales nous démontrons des propriétés universelles des fonctions
de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes
avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec
des réservoirs à droite et à gauche.
acknowledgement: The authors would like to thank Gioia Carinci and Cristian Giardinà
for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT
(Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay
University), where part of this work was performed. S.F. acknowledges Simona Villa
for her support in creating the picture. S.F. acknowledges financial support from
NWO via the grant TOP1.17.019. F.S. acknowledges financial support from 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
author:
- first_name: Simone
full_name: Floreani, Simone
last_name: Floreani
- first_name: Frank
full_name: Redig, Frank
last_name: Redig
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Floreani S, Redig F, Sau F. Orthogonal polynomial duality of boundary driven
particle systems and non-equilibrium correlations. Annales de l’institut Henri
Poincare (B) Probability and Statistics. 2022;58(1):220-247. doi:10.1214/21-AIHP1163
apa: Floreani, S., Redig, F., & Sau, F. (2022). Orthogonal polynomial duality
of boundary driven particle systems and non-equilibrium correlations. Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics. https://doi.org/10.1214/21-AIHP1163
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial
Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.”
Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163.
ieee: S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary
driven particle systems and non-equilibrium correlations,” Annales de l’institut
Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of
Mathematical Statistics, pp. 220–247, 2022.
ista: Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary
driven particle systems and non-equilibrium correlations. Annales de l’institut
Henri Poincare (B) Probability and Statistics. 58(1), 220–247.
mla: Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven
Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri
Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical
Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163.
short: S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability
and Statistics 58 (2022) 220–247.
date_created: 2022-02-27T23:01:50Z
date_published: 2022-02-01T00:00:00Z
date_updated: 2023-10-17T12:49:43Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AIHP1163
ec_funded: 1
external_id:
arxiv:
- '2007.08272'
isi:
- '000752489300010'
intvolume: ' 58'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2007.08272
month: '02'
oa: 1
oa_version: Preprint
page: 220-247
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium
correlations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2022'
...
---
_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
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.
date_created: 2022-05-08T22:01:44Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2023-10-17T12:50:24Z
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: '10023'
abstract:
- lang: eng
text: We study the temporal dissipation of variance and relative entropy for ergodic
Markov Chains in continuous time, and compute explicitly the corresponding dissipation
rates. These are identified, as is well known, in the case of the variance in
terms of an appropriate Hilbertian norm; and in the case of the relative entropy,
in terms of a Dirichlet form which morphs into a version of the familiar Fisher
information under conditions of detailed balance. Here we obtain trajectorial
versions of these results, valid along almost every path of the random motion
and most transparent in the backwards direction of time. Martingale arguments
and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer
and Tschiderer for conservative diffusions. Extensions are developed to general
“convex divergences” and to countable state-spaces. The steepest descent and gradient
flow properties for the variance, the relative entropy, and appropriate generalizations,
are studied along with their respective geometries under conditions of detailed
balance, leading to a very direct proof for the HWI inequality of Otto and Villani
in the present context.
acknowledgement: I.K. acknowledges support from the U.S. National Science Foundation
under Grant NSF-DMS-20-04997. J.M. acknowledges support from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 716117) and from the Austrian Science Fund (FWF) through project
F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant
P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008
and MA16-021.
article_processing_charge: No
article_type: original
author:
- first_name: Ioannis
full_name: Karatzas, Ioannis
last_name: Karatzas
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Walter
full_name: Schachermayer, Walter
last_name: Schachermayer
citation:
ama: Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient
flow for the relative entropy in Markov chains. Communications in Information
and Systems. 2021;21(4):481-536. doi:10.4310/CIS.2021.v21.n4.a1
apa: Karatzas, I., Maas, J., & Schachermayer, W. (2021). Trajectorial dissipation
and gradient flow for the relative entropy in Markov chains. Communications
in Information and Systems. International Press. https://doi.org/10.4310/CIS.2021.v21.n4.a1
chicago: Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation
and Gradient Flow for the Relative Entropy in Markov Chains.” Communications
in Information and Systems. International Press, 2021. https://doi.org/10.4310/CIS.2021.v21.n4.a1.
ieee: I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and
gradient flow for the relative entropy in Markov chains,” Communications in
Information and Systems, vol. 21, no. 4. International Press, pp. 481–536,
2021.
ista: Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient
flow for the relative entropy in Markov chains. Communications in Information
and Systems. 21(4), 481–536.
mla: Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the
Relative Entropy in Markov Chains.” Communications in Information and Systems,
vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:10.4310/CIS.2021.v21.n4.a1.
short: I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and
Systems 21 (2021) 481–536.
date_created: 2021-09-19T08:53:19Z
date_published: 2021-06-04T00:00:00Z
date_updated: 2021-09-20T12:51:18Z
day: '04'
department:
- _id: JaMa
doi: 10.4310/CIS.2021.v21.n4.a1
ec_funded: 1
external_id:
arxiv:
- '2005.14177'
intvolume: ' 21'
issue: '4'
keyword:
- Markov Chain
- relative entropy
- time reversal
- steepest descent
- gradient flow
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2005.14177
month: '06'
oa: 1
oa_version: Preprint
page: 481-536
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: Communications in Information and Systems
publication_identifier:
issn:
- 1526-7555
publication_status: published
publisher: International Press
quality_controlled: '1'
status: public
title: Trajectorial dissipation and gradient flow for the relative entropy in Markov
chains
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 21
year: '2021'
...
---
_id: '10613'
abstract:
- lang: eng
text: Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci,
and Redig, we first provide a general framework for the study of scaling limits
of higher-order fields. Then, by considering the same class of infinite interacting
particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion
and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic
limit, and convergence for the equilibrium fluctuations, of higher-order fields.
In particular, the limit fields exhibit a tensor structure. Our fluctuation result
differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional
Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium
fluctuations, of higher-order fields. In particular, the limit fields exhibit
a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}],
since we consider a different notion of higher-order fluctuation fields.
acknowledgement: "F.S. would like to thank Mario Ayala and Frank Redig for useful
discussions. J.P.C. acknowledges partial financial support from the US National
Science Foundation (DMS-1855604). F.S. was financially supported by the European
Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie
grant agreement No. 754411.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Joe P.
full_name: Chen, Joe P.
last_name: Chen
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of
interacting particle systems. Markov Processes And Related Fields. 2021;27(3):339-380.
apa: Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium
fluctuations of interacting particle systems. Markov Processes And Related
Fields. Polymat Publishing.
chicago: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields. Polymat Publishing, 2021.
ieee: J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems,” Markov Processes And Related Fields,
vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.
ista: Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.
mla: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.
short: J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.
date_created: 2022-01-10T14:02:31Z
date_published: 2021-03-16T00:00:00Z
date_updated: 2022-01-10T15:29:08Z
day: '16'
department:
- _id: JaMa
ec_funded: 1
external_id:
arxiv:
- '2008.13403'
intvolume: ' 27'
issue: '3'
keyword:
- interacting particle systems
- higher-order fields
- hydrodynamic limit
- equilibrium fluctuations
- duality
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/2008.13403
month: '03'
oa: 1
oa_version: Preprint
page: 339-380
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Markov Processes And Related Fields
publication_identifier:
issn:
- 1024-2953
publication_status: published
publisher: Polymat Publishing
quality_controlled: '1'
related_material:
link:
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relation: other
url: http://math-mprf.org/journal/articles/id1614/
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relation: used_for_analysis_in
url: https://arxiv.org/abs/2004.08412
status: public
title: Higher-order hydrodynamics and equilibrium fluctuations of interacting particle
systems
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...
---
_id: '9973'
abstract:
- lang: eng
text: In this article we introduce a complete gradient estimate for symmetric quantum
Markov semigroups on von Neumann algebras equipped with a normal faithful tracial
state, which implies semi-convexity of the entropy with respect to the recently
introduced noncommutative 2-Wasserstein distance. We show that this complete gradient
estimate is stable under tensor products and free products and establish its validity
for a number of examples. As an application we prove a complete modified logarithmic
Sobolev inequality with optimal constant for Poisson-type semigroups on free group
factors.
acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions
and helpful comments.
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
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4
apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov
semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics. Springer Nature,
2021. https://doi.org/10.1007/s00220-021-04199-4.
ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 387. Springer Nature, pp.
761–791, 2021.
ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 387, 761–791.
mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer
Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.
short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.
date_created: 2021-08-30T10:07:44Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2023-08-11T11:09:07Z
day: '30'
ddc:
- '621'
department:
- _id: JaMa
doi: 10.1007/s00220-021-04199-4
ec_funded: 1
external_id:
arxiv:
- '2007.13506'
isi:
- '000691214200001'
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file_size: 505971
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keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 761–791
project:
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name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: 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: Complete gradient estimates of 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 387
year: '2021'
...
---
_id: '10024'
abstract:
- lang: eng
text: In this paper, we introduce a random environment for the exclusion process
in obtained by assigning a maximal occupancy to each site. This maximal occupancy
is allowed to randomly vary among sites, and partial exclusion occurs. Under the
assumption of ergodicity under translation and uniform ellipticity of the environment,
we derive a quenched hydrodynamic limit in path space by strengthening the mild
solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose,
we prove, employing the technology developed for the random conductance model,
a homogenization result in the form of an arbitrary starting point quenched invariance
principle for a single particle in the same environment, which is a result of
independent interest. The self-duality property of the partial exclusion process
allows us to transfer this homogenization result to the particle system and, then,
apply the tightness criterion in Redig et al. (2020).
acknowledgement: The authors would like to thank Marek Biskup and Alberto Chiarini
for useful suggestions and Cristian Giardina, Frank den Hollander and Shubhamoy Nandan for inspiring discussions. S.F. acknowledges Simona Villa for her help in creating the picture. Furthermore,
the authors thank two anonymous referees for the careful reading of the manuscript. S.F.
acknowledges financial support from NWO, The Netherlands via the grant TOP1.17.019.
F.S. acknowledges financial support from NWO via the TOP1 grant 613.001.552 as well as
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie-Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes
article_type: original
author:
- first_name: Simone
full_name: Floreani, Simone
last_name: Floreani
- first_name: Frank
full_name: Redig, Frank
last_name: Redig
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process
in random environment. Stochastic Processes and their Applications. 2021;142:124-158.
doi:10.1016/j.spa.2021.08.006
apa: Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial
exclusion process in random environment. Stochastic Processes and Their Applications.
Elsevier. https://doi.org/10.1016/j.spa.2021.08.006
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the
Partial Exclusion Process in Random Environment.” Stochastic Processes and
Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.
ieee: S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion
process in random environment,” Stochastic Processes and their Applications,
vol. 142. Elsevier, pp. 124–158, 2021.
ista: Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion
process in random environment. Stochastic Processes and their Applications. 142,
124–158.
mla: Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in
Random Environment.” Stochastic Processes and Their Applications, vol.
142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.
short: S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications
142 (2021) 124–158.
date_created: 2021-09-19T22:01:25Z
date_published: 2021-08-27T00:00:00Z
date_updated: 2023-08-14T06:52:43Z
day: '27'
ddc:
- '519'
department:
- _id: JaMa
doi: 10.1016/j.spa.2021.08.006
ec_funded: 1
external_id:
arxiv:
- '1911.12564'
isi:
- '000697748500005'
file:
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checksum: 56768c553d7218ee5714902ffec90ec4
content_type: application/pdf
creator: dernst
date_created: 2022-05-13T07:55:50Z
date_updated: 2022-05-13T07:55:50Z
file_id: '11370'
file_name: 2021_StochasticProcessesAppl_Floreani.pdf
file_size: 2115791
relation: main_file
success: 1
file_date_updated: 2022-05-13T07:55:50Z
has_accepted_license: '1'
intvolume: ' 142'
isi: 1
keyword:
- hydrodynamic limit
- random environment
- random conductance model
- arbitrary starting point quenched invariance principle
- duality
- mild solution
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 124-158
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Stochastic Processes and their Applications
publication_identifier:
issn:
- 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hydrodynamics for the partial exclusion process in random environment
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: 142
year: '2021'
...
---
_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
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).
date_created: 2021-10-03T22:01:21Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-14T07:05:44Z
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'
...
---
_id: '9627'
abstract:
- lang: eng
text: "We compute the deficiency spaces of operators of the form \U0001D43B\U0001D434⊗̂
\U0001D43C+\U0001D43C⊗̂ \U0001D43B\U0001D435, for symmetric \U0001D43B\U0001D434
and self-adjoint \U0001D43B\U0001D435. This enables us to construct self-adjoint
extensions (if they exist) by means of von Neumann's theory. The structure of
the deficiency spaces for this case was asserted already in Ibort et al. [Boundary
dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301],
but only proven under the restriction of \U0001D43B\U0001D435 having discrete,
non-degenerate spectrum."
acknowledgement: M. W. gratefully acknowledges financial support by the German Academic
Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom
Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA
GmbH for their financial support in the form of scholarships during his Master's
and Bachelor's studies respectively. The authors want to thank Mark Malamud for
pointing out the reference [1] to them. This work was supported by the Ministry
of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.
article_processing_charge: No
article_type: original
author:
- first_name: Daniel
full_name: Lenz, Daniel
last_name: Lenz
- first_name: Timon
full_name: Weinmann, Timon
last_name: Weinmann
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians.
Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447.
doi:10.1017/S0013091521000080
apa: Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of
bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society.
Cambridge University Press. https://doi.org/10.1017/S0013091521000080
chicago: Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions
of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society.
Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080.
ieee: D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite
Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol.
64, no. 3. Cambridge University Press, pp. 443–447, 2021.
ista: Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians.
Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.
mla: Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings
of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University
Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080.
short: D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical
Society 64 (2021) 443–447.
date_created: 2021-07-04T22:01:24Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2023-08-17T07:12:05Z
day: '01'
department:
- _id: JaMa
doi: 10.1017/S0013091521000080
external_id:
arxiv:
- '1912.03670'
isi:
- '000721363700003'
intvolume: ' 64'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1017/S0013091521000080
month: '08'
oa: 1
oa_version: Published Version
page: 443-447
publication: Proceedings of the Edinburgh Mathematical Society
publication_identifier:
eissn:
- 1464-3839
issn:
- 0013-0915
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Self-adjoint extensions of bipartite Hamiltonians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2021'
...