The Monge-Kantorovich problem: achievements, connections, and perspectives
VI Bogachev, AV Kolesnikov - Russian Mathematical Surveys, 2012 - iopscience.iop.org
This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …
Principle results are presented on the existence of solutions and their properties both in the …
[图书][B] Optimal transport: old and new
C Villani - 2009 - Springer
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …
John Mather launched a revolution in the venerable field of optimal transport founded by G …
Задача Монжа–Канторовича: достижения, связи и перспективы
ВИ Богачев, АВ Колесников - Успехи математических наук, 2012 - mathnet.ru
В статье дается обзор недавних исследований, связанных с задачей Монжа-
Канторовича. Приведены основные результаты о существовании решений и их …
Канторовича. Приведены основные результаты о существовании решений и их …
On the role of convexity in isoperimetry, spectral gap and concentration
E Milman - Inventiones mathematicae, 2009 - Springer
We show that for convex domains in Euclidean space, Cheeger's isoperimetric inequality,
spectral gap of the Neumann Laplacian, exponential concentration of Lipschitz functions …
spectral gap of the Neumann Laplacian, exponential concentration of Lipschitz functions …
Transport inequalities. A survey
N Gozlan, C Léonard - arXiv preprint arXiv:1003.3852, 2010 - arxiv.org
arXiv:1003.3852v1 [math.PR] 19 Mar 2010 Page 1 arXiv:1003.3852v1 [math.PR] 19 Mar 2010
TRANSPORT INEQUALITIES. A SURVEY NATHAEL GOZLAN, CHRISTIAN LÉONARD …
TRANSPORT INEQUALITIES. A SURVEY NATHAEL GOZLAN, CHRISTIAN LÉONARD …
Sharp isoperimetric inequalities and model spaces for the curvature-dimension-diameter condition
E Milman - Journal of the European Mathematical Society, 2015 - ems.press
We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a
probability measure, whose generalized Ricci curvature is bounded from below (possibly …
probability measure, whose generalized Ricci curvature is bounded from below (possibly …
Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality
N Datta, C Rouzé - Annales Henri Poincaré, 2020 - Springer
Quantum Markov semigroups characterize the time evolution of an important class of open
quantum systems. Studying convergence properties of such a semigroup and determining …
quantum systems. Studying convergence properties of such a semigroup and determining …
Fisher information and logarithmic Sobolev inequality for matrix-valued functions
L Gao, M Junge, N LaRacuente - Annales Henri Poincaré, 2020 - Springer
We prove a version of Talagrand's concentration inequality for subordinated sub-Laplacians
on a compact Riemannian manifold using tools from noncommutative geometry. As an …
on a compact Riemannian manifold using tools from noncommutative geometry. As an …
Quantitative logarithmic Sobolev inequalities and stability estimates
We establish an improved form of the classical logarithmic Sobolev inequality for the
Gaussian measure restricted to probability densities which satisfy a Poincar\'e inequality …
Gaussian measure restricted to probability densities which satisfy a Poincar\'e inequality …
[HTML][HTML] Bounds on the deficit in the logarithmic Sobolev inequality
Bounds on the deficit in the logarithmic Sobolev inequality - ScienceDirect Skip to main
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