A concentration theorem for the equilibrium measure of Markov chains with nonnegative coarse Ricci curvature - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2012

A concentration theorem for the equilibrium measure of Markov chains with nonnegative coarse Ricci curvature

Résumé

A nonnegative coarse Ricci curvature for a Markov chain and the existence of an attractive point implies the concentration of the invariant probability measure around this point. The mass outside balls centered at the attractive point, as a function of the radius, decreases at least as fast as the exponential of a double integral of the coarse Ricci curvature. This is exactly the behaviour of the density of the reversible measure for diffusion processes on the real line.
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Dates et versions

hal-00678728 , version 1 (13-03-2012)

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Laurent Veysseire. A concentration theorem for the equilibrium measure of Markov chains with nonnegative coarse Ricci curvature. 2012. ⟨hal-00678728⟩
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