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

Laurent Veysseire (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Mots clés: Markov chain; coarse Ricci curvature; concentration of measure

Domaines: Probabilités [math.PR]

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