Contractive coupling rates and curvature lower bounds for Markov chains
Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv, 10.48550/arXiv.2308.00516.
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https://doi.org/10.48550/arXiv.2308.00516
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Abstract
Contractive coupling rates have been recently introduced by Conforti as a
tool to establish convex Sobolev inequalities (including modified log-Sobolev
and Poincar\'{e} inequality) for some classes of Markov chains. In this work,
we show how contractive coupling rates can also be used to prove stronger
inequalities, in the form of curvature lower bounds for Markov chains and
geodesic convexity of entropic functionals. We illustrate this in several
examples discussed by Conforti, where in particular, after appropriately
choosing a parameter function, we establish positive curvature in the entropic
and (discrete) Bakry--\'{E}mery sense. In addition, we recall and give
straightforward generalizations of some notions of coarse Ricci curvature, and
we discuss some of their properties and relations with the concepts of
couplings and coupling rates: as an application, we show exponential
contraction of the $p$-Wasserstein distance for the heat flow in the
aforementioned examples.
Publishing Year
Date Published
2023-08-02
Journal Title
arXiv
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Cite this
Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv. doi:10.48550/arXiv.2308.00516
Pedrotti, F. (n.d.). Contractive coupling rates and curvature lower bounds for Markov chains. arXiv. https://doi.org/10.48550/arXiv.2308.00516
Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2308.00516.
F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” arXiv. .
Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv, 10.48550/arXiv.2308.00516.
Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” ArXiv, doi:10.48550/arXiv.2308.00516.
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arXiv 2308.00516