A probabilistic approach to convex \((\phi)\)-entropy decay for Markov chains

DOI10.1214/21-AAP1700zbMath1491.37008arXiv2004.10850OpenAlexW4225137434MaRDI QIDQ2134287

Giovanni Conforti

Publication date: 6 May 2022

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.10850

zbMATH Keywords

Markov chainsSobolev inequalityGlauber dynamicscouplingentropy functionalsBakry-Émery methodBeckner inequalitiesconvexity of the entropydiscrete convex Sobolev inequalitiesexponential dissipationhardcore models

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Functional inequalities, including subadditivity, convexity, etc. (39B62) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) General theory of functional equations and inequalities (39B05) Dynamical aspects of statistical mechanics (37A60)

Related Items (3)

Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics ⋮ Upgrading MLSI to LSI for reversible Markov chains ⋮ On mixing of Markov chains: coupling, spectral independence, and entropy factorization

Cites Work

• Unnamed Item
• Unnamed Item
• Entropic Ricci curvature bounds for discrete interacting systems
• Geodesic convexity of the relative entropy in reversible Markov chains
• Entropy decay for interacting systems via the Bochner-Bakry-Émery approach
• Displacement convexity of entropy and related inequalities on graphs
• Ricci curvature bounds for weakly interacting Markov chains
• Gradient flows of the entropy for finite Markov chains
• Convex entropy decay via the Bochner-Bakry-Emery approach
• Modified logarithmic Sobolev inequalities in discrete settings
• Ricci curvature of Markov chains on metric spaces
• Inequalities in Fourier analysis
• On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups
• Exponential decay of entropy in the random transposition and Bernoulli-Laplace models
• A note on the Glauber dynamics for sampling independent sets
• Discrete Beckner inequalities via the Bochner-Bakry-Emery approach for Markov chains
• A discrete log-Sobolev inequality under a Bakry-Émery type condition
• Ricci curvature of finite Markov chains via convexity of the entropy
• Logarithmic Sobolev inequalities and stochastic Ising models
• Entropy dissipation estimates for inhomogeneous zero-range processes
• Spectral gap estimates for interacting particle systems via a Bochner-type identity
• Modified logarithmic Sobolev inequalities for some models of random walk
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• A Generalized Poincare Inequality for Gaussian Measures
• Markov Chains
• Optimal markovian couplings and applications
• Fast convergence of the Glauber dynamics for sampling independent sets
• Time to Reach Stationarity in the Bernoulli–Laplace Diffusion Model
• Analysis and Geometry of Markov Diffusion Operators
• On Markov Chains for Independent Sets
• Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
• Optimal Transport
• Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models

This page was built for publication: A probabilistic approach to convex \((\phi)\)-entropy decay for Markov chains