ESAIM - Probability and Statistics, ISSN 1292-8100, 2017, Volume 21, pp. 467 - 494

We study a class of logarithmic Sobolev inequalities with a general form of the energy functional...

Concentration of measure | Modified logarithmic Sobolev inequalities | POINCARE | SPACES | CHAOSES | STATISTICS & PROBABILITY | modified logarithmic Sobolev inequalities | LOGARITHMICALLY CONCAVE TAILS | INDEPENDENT RANDOM-VARIABLES | SUMS | Norms | Euclidean geometry | Euclidean space | Inequalities | Inequality

Concentration of measure | Modified logarithmic Sobolev inequalities | POINCARE | SPACES | CHAOSES | STATISTICS & PROBABILITY | modified logarithmic Sobolev inequalities | LOGARITHMICALLY CONCAVE TAILS | INDEPENDENT RANDOM-VARIABLES | SUMS | Norms | Euclidean geometry | Euclidean space | Inequalities | Inequality

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

MATHEMATICS | COUNTS | MATHEMATICS, APPLIED | modified logarithmic Sobolev inequality | LOGARITHMIC SOBOLEV INEQUALITIES | improved Poincare inequality | Hypercontractivity | superconcentration | Poisson processes

Journal Article

Probability theory and related fields, ISSN 1432-2064, 2013, Volume 160, Issue 1-2, pp. 47 - 94

... Prékopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HWI type as well as log-Sobolev type inequalities in discrete settings...

Transport inequalities | 60E15 | 32F32 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Displacement convexity | Modified logarithmic-Sobolev inequalities | Statistics for Business/Economics/Mathematical Finance/Insurance | 39A12 | Operations Research/Decision Theory | Ricci curvature | METRIC-MEASURE-SPACES | LOGARITHMIC SOBOLEV INEQUALITIES | MARKOV-CHAINS | TRANSPORTATION | INFORMATION | PROBABILITY-MEASURES | STATISTICS & PROBABILITY | BERNOULLI | BRASCAMP | GEOMETRY | Computer science | Studies | Probability | Convex analysis | Mathematical analysis | Inequalities | Constants | Graphs | Gaussian | Entropy | Convexity | Displacement | Functional Analysis

Transport inequalities | 60E15 | 32F32 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Displacement convexity | Modified logarithmic-Sobolev inequalities | Statistics for Business/Economics/Mathematical Finance/Insurance | 39A12 | Operations Research/Decision Theory | Ricci curvature | METRIC-MEASURE-SPACES | LOGARITHMIC SOBOLEV INEQUALITIES | MARKOV-CHAINS | TRANSPORTATION | INFORMATION | PROBABILITY-MEASURES | STATISTICS & PROBABILITY | BERNOULLI | BRASCAMP | GEOMETRY | Computer science | Studies | Probability | Convex analysis | Mathematical analysis | Inequalities | Constants | Graphs | Gaussian | Entropy | Convexity | Displacement | Functional Analysis

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

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

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

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

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

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

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

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

We introduce a new Harnack type inequality, which is a modification of the log-Harnack inequality established...

60J75 | Modified log-Harnack inequality | Strong Feller property | 2D stochastic Navier-Stokes equation | Log-Harnack inequality | Analysis | Mathematics | Wang type Harnack inequality | Asymptotically strong Feller property | 60J45 | Asymptotic coupling | ERGODICITY | MATHEMATICS, APPLIED | LOGARITHMIC SOBOLEV INEQUALITIES | TIME ASYMPTOTICS | MATHEMATICS | SEMIGROUPS | NAVIER-STOKES EQUATIONS | MANIFOLDS | Equality

60J75 | Modified log-Harnack inequality | Strong Feller property | 2D stochastic Navier-Stokes equation | Log-Harnack inequality | Analysis | Mathematics | Wang type Harnack inequality | Asymptotically strong Feller property | 60J45 | Asymptotic coupling | ERGODICITY | MATHEMATICS, APPLIED | LOGARITHMIC SOBOLEV INEQUALITIES | TIME ASYMPTOTICS | MATHEMATICS | SEMIGROUPS | NAVIER-STOKES EQUATIONS | MANIFOLDS | Equality

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

STATISTICS & PROBABILITY | concentration inequalities | SUPREMA | modified logarithmic Sobolev inequalities | matrix Bernstein inequality | Rademacher chaos | uniform Hanson-Wright inequalities

Journal Article

Potential Analysis, ISSN 0926-2601, 2009, Volume 31, Issue 2, pp. 183 - 202

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 11/2018, Volume 142, pp. 30 - 38

In this paper, we study strong modified transportation cost inequalities for k-concave probability measures with heavy tails...

Tensorization | Strong modified transportation cost inequalities | Polynomial-type concentration inequalities | Dual representation | [formula omitted]-concave probability measures | k-concave probability measures | LOGARITHMIC SOBOLEV INEQUALITIES | STATISTICS & PROBABILITY

Tensorization | Strong modified transportation cost inequalities | Polynomial-type concentration inequalities | Dual representation | [formula omitted]-concave probability measures | k-concave probability measures | LOGARITHMIC SOBOLEV INEQUALITIES | STATISTICS & PROBABILITY

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 9/2007, Volume 139, Issue 1, pp. 65 - 87

..., uniformly over the number of particles and the number of vertices. Keywords Zero-range dynamics · Entropy dissipation · Modi ed logarithmic Sobolev inequalities...

Entropy dissipation | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Mathematical and Computational Physics | Zero-range dynamics | Modified logarithmic Sobolev inequalities | Probability Theory and Stochastic Processes | Mathematics | Mathematical Biology in General | 60K35 | Quantitative Finance | LOGARITHMIC SOBOLEV INEQUALITY | MODELS | KAWASAKI DYNAMICS | SPIN SYSTEMS | STATISTICS & PROBABILITY | zero-range dynamics | SPECTRAL GAP | BERNOULLI | modified logarithmic Sobolev inequalities | entropy dissipation | Studies | Probability | Entropy | Models

Entropy dissipation | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Mathematical and Computational Physics | Zero-range dynamics | Modified logarithmic Sobolev inequalities | Probability Theory and Stochastic Processes | Mathematics | Mathematical Biology in General | 60K35 | Quantitative Finance | LOGARITHMIC SOBOLEV INEQUALITY | MODELS | KAWASAKI DYNAMICS | SPIN SYSTEMS | STATISTICS & PROBABILITY | zero-range dynamics | SPECTRAL GAP | BERNOULLI | modified logarithmic Sobolev inequalities | entropy dissipation | Studies | Probability | Entropy | Models

Journal Article

16.
Full Text
Exponential Decay of Entropy in the Random Transposition and Bernoulli: Laplace Models

The Annals of Applied Probability, ISSN 1050-5164, 11/2003, Volume 13, Issue 4, pp. 1591 - 1600

We give bounds on the exponential decay rate of entropy in the random transposition model and the Bernoulli-Laplace model which are independent of the number...

Statistical models | Random walk | Probability theory | Markov processes | Entropy | Mathematical inequalities | Density distributions | Mathematical models | Modified logarithmic Sobolev inequality | Time to stationarity | modified logarithmic Sobolev inequality | LOGARITHMIC SOBOLEV INEQUALITIES | RANDOM-WALKS | STATISTICS & PROBABILITY | time to stationarity | DIFFUSION | TIME | SIMPLE EXCLUSION PROCESSES | 60B15 | 60K35 | 60J22

Statistical models | Random walk | Probability theory | Markov processes | Entropy | Mathematical inequalities | Density distributions | Mathematical models | Modified logarithmic Sobolev inequality | Time to stationarity | modified logarithmic Sobolev inequality | LOGARITHMIC SOBOLEV INEQUALITIES | RANDOM-WALKS | STATISTICS & PROBABILITY | time to stationarity | DIFFUSION | TIME | SIMPLE EXCLUSION PROCESSES | 60B15 | 60K35 | 60J22

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 06/2003, Volume 126, Issue 3, pp. 395 - 420

.... We also describe contraction bounds in the entropy sense around arbitrary probability measures by introducing a suitable Dirichlet form and the corresponding modified logarithmic Sobolev constants...

Generalized relative entropy | Modified logarithmic Sobolev inequality | Lipschitz contraction | Spectral gap | Markov kernel | Orlicz norm | Dirichlet form | Dobrushin's ergodic coefficient | Inhomogeneous Gaussian chains | Loose of memory property | generalized relative entropy | modified logarithmic Sobolev inequality inhomogeneous Gaussian chains | spectral gap | loose of memory property | STATISTICS & PROBABILITY

Generalized relative entropy | Modified logarithmic Sobolev inequality | Lipschitz contraction | Spectral gap | Markov kernel | Orlicz norm | Dirichlet form | Dobrushin's ergodic coefficient | Inhomogeneous Gaussian chains | Loose of memory property | generalized relative entropy | modified logarithmic Sobolev inequality inhomogeneous Gaussian chains | spectral gap | loose of memory property | STATISTICS & PROBABILITY

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

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

The Annals of Applied Probability, ISSN 1050-5164, 11/2002, Volume 12, Issue 4, pp. 1492 - 1515

In 1999 Catoni determined the critical rate H3 for the relaxation time of generalized Metropolis algorithms, models for which the speed of convergence to...

Ergodic theory | Constant coefficients | Simulated annealing | Respect | Metropolitan areas | Markov chains | Infrared radiation | Mathematics | Mathematical minima | Low temperature | Critical rate for relaxation times | Spectral gaps and singular values | Generalized Metropolis algorithm at low temperature | Delaying effect for ergodic constants | Classical or modified logarithmic Sobolev inequalities | Dobrushin's coefficient and coupling | generalized Metropolis algorithm at low temperature | delaying effect for ergodic constants | simulated annealing | spectral gaps and singular values | classical or modified logarithmic Sobolev inequalities | STATISTICS & PROBABILITY | SIMULATED ANNEALING ALGORITHMS | critical rate for relaxation times | 60J10 | 49K45 | 65C40 | 37A25 | 15A18

Ergodic theory | Constant coefficients | Simulated annealing | Respect | Metropolitan areas | Markov chains | Infrared radiation | Mathematics | Mathematical minima | Low temperature | Critical rate for relaxation times | Spectral gaps and singular values | Generalized Metropolis algorithm at low temperature | Delaying effect for ergodic constants | Classical or modified logarithmic Sobolev inequalities | Dobrushin's coefficient and coupling | generalized Metropolis algorithm at low temperature | delaying effect for ergodic constants | simulated annealing | spectral gaps and singular values | classical or modified logarithmic Sobolev inequalities | STATISTICS & PROBABILITY | SIMULATED ANNEALING ALGORITHMS | critical rate for relaxation times | 60J10 | 49K45 | 65C40 | 37A25 | 15A18

Journal Article

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

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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