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ESAIM - Probability and Statistics, ISSN 1292-8100, 2017, Volume 21, pp. 467 - 494
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2020, Volume 148, Issue 8, pp. 3617 - 3632
.... We deduce from this result some versions of Talagrand's L^1- L^2 inequality for increasing and concave mappings, and we build examples showing that such an estimate represents a strict improvement of the classical Poincaré inequality... 
MATHEMATICS | COUNTS | MATHEMATICS, APPLIED | modified logarithmic Sobolev inequality | LOGARITHMIC SOBOLEV INEQUALITIES | improved Poincare inequality | Hypercontractivity | superconcentration | Poisson processes
Journal Article
Potential Analysis, ISSN 0926-2601, 10/2011, Volume 35, Issue 3, pp. 275 - 286
A criterion is presented for the Modified Logarithmic Sobolev inequality on metric measure spaces... 
Geometry | 60E15 | Potential Theory | Functional Analysis | 26D10 | Probability Theory and Stochastic Processes | U bounds | Mathematics | Modified Logarithmic Sobolev inequality | MATHEMATICS | Equality
Journal Article
ESAIM - Probability and Statistics, ISSN 1292-8100, 2015, Volume 19, pp. 544 - 559
In this paper, we prove modified logarithmic Sobolev inequalities for canonical ensembles with superquadratic single-site potential... 
Modified logarithmic Sobolev inequalities | Coarse-graining | Spin system | spin system | STATISTICS & PROBABILITY | coarse-graining | Inequalities | Probability | Mathematics | Functional Analysis | Mathematical Physics | Analysis of PDEs
Journal Article
Potential Analysis, ISSN 0926-2601, 2/2018, Volume 48, Issue 2, pp. 125 - 157
.... As a main application, the hypercontractivity of this class of infimal-convolution operators is connected to some discrete version of the log-Sobolev inequality and to a discrete version... 
Geometry | Modified Log-Sob inequalities on graphs | 70H20 | Hamilton-Jacobi equations | Potential Theory | Functional Analysis | 35F21 | Weak-transport entropy inequalities | Probability Theory and Stochastic Processes | Mathematics | 35R02 | 37L50 | MATHEMATICS | TRANSPORT | LOGARITHMIC SOBOLEV INEQUALITIES | MARKOV-CHAINS | SPACES | ENTROPY
Journal Article
Electronic Journal of Probability, ISSN 1083-6489, 2013, Volume 18, pp. 1 - 21
We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We... 
Modified logarithmic sobolev inequality | Stochastic particle systems | Entropy decay | Modified logarithmic Sobolev inequality | LOGARITHMIC SOBOLEV INEQUALITIES | DYNAMICS | STATISTICS & PROBABILITY | SPECTRAL GAP
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 08/2009, Volume 45, Issue 3, pp. 734 - 753
We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov... 
Modified logarithmic Sobolev inequality | Stochastic particle systems | Entropy decay | LOGARITHMIC SOBOLEV INEQUALITIES | MODELS | ZERO-RANGE DYNAMICS | STATISTICS & PROBABILITY | SPECTRAL GAP | BERNOULLI | LATTICE | UNBOUNDED SPIN SYSTEMS | 39B62 | 60K35 | 60J80
Journal Article
Electronic Journal of Probability, ISSN 1083-6489, 2017, Volume 22
We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain... 
Markov chain | Modified logarithmic Sobolev inequality | Random walk | Hardcore model | Ricci curvature | Ising model | Cayley graph | METRIC-MEASURE-SPACES | INEQUALITIES | STATISTICS & PROBABILITY | INDEPENDENT SETS | random walk | modified logarithmic Sobolev inequality | SYSTEMS | hardcore model | ENTROPY
Journal Article
POTENTIAL ANALYSIS, ISSN 0926-2601, 08/2009, Volume 31, Issue 2, pp. 183 - 202
In this paper, the modified logarithmic Sobolev inequalities and transportation cost inequalities for measures with density e(-V... 
MATHEMATICS | Prekopa-Leindler inequalities | Transportation cost inequalities | LOG-SOBOLEV | POINCARE | Modified logarithmic Sobolev inequalities | BRUNN-MINKOWSKI | BRASCAMP | Hamilton-Jacobi semigroups
Journal Article
Journal of evolution equations, ISSN 1424-3202, 2011, Volume 11, Issue 4, pp. 925 - 942
Journal Article
ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2020, Volume 25
This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector X is an element of R-n with independent subgaussian components... 
STATISTICS & PROBABILITY | concentration inequalities | SUPREMA | modified logarithmic Sobolev inequalities | matrix Bernstein inequality | Rademacher chaos | uniform Hanson-Wright inequalities
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 11/2018, Volume 142, pp. 30 - 38
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 11/2003, Volume 13, Issue 4, pp. 1591 - 1600
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 06/2003, Volume 126, Issue 3, pp. 395 - 420
Journal Article
Lecture Notes in Mathematics, ISSN 0075-8434, 2009, Volume 1979, pp. 103 - 130
.... We study the discrete and continuous settings (and their relationships); we are interested in Poincare or logarithmic Sobolev inequalities, and several variants... 
Linear diffusions | Monotonicity of extremal functions | (modified) logarithmic Sobolev inequality | Birth and death process | Poincarè inequality | birth and death process | EIGENVALUE | MATHEMATICS | monotonicity of extremal functions | linear diffusions | Poincare inequality | SPECTRUM | OPERATORS
Conference Proceeding
Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 278, Issue 1, pp. 173 - 199
.... As an application, we prove that the optimal logarithmic Sobolev constant on compact manifolds equipped with the K-super m-dimensional Bakry Emery Ricci flow is decreasing in time. 
Witten Laplacian | W-entropy | modified Ricci flow | Bakry-émery Ricci curvature | EIGENVALUE | MATHEMATICS | TRANSPORT | HEAT-EQUATION | CURVATURE | MONOTONICITY | EMERY-RICCI TENSOR | POROUS-MEDIUM | HARNACK INEQUALITIES | FAST DIFFUSION-EQUATIONS | COMPLETE RIEMANNIAN-MANIFOLDS | Mathematics - Differential Geometry
Journal Article
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