Exponential convergence rate in entropy

DOI10.1007/S11464-007-0022-5zbMath1152.60059OpenAlexW2015372942MaRDI QIDQ934349

Chen Mu-Fa

Publication date: 29 July 2008

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-007-0022-5

zbMATH Keywords

Markov chainspectral gapsymmetric formlogarithmic Sobolev constantExponential convergence rate

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Continuous-time Markov processes on discrete state spaces (60J27)

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Transport-information inequalities for Markov chains ⋮ Unified speed estimation of various stabilities

Cites Work

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• Modified logarithmic Sobolev inequalities in discrete settings
• Coupling, spectral gap and related topics. III
• Logarithmic Sobolev inequality for symmetric forms
• Exponential convergence rate in Boltzmann-Shannon entropy
• Nash inequalities for general symmetric forms
• Functional inequalities for empty essential spectrum
• Logarithmic Sobolev inequalities for finite Markov chains
• Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
• ExponentialL 2-convergence andL 2-spectral gap for Markov processes
• Estimation of spectral gap for Markov chains
• Sobolev type inequalities for general symmetric forms
• Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap

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