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

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

2012-03-13

arxiv.org/abs/1203.2897v1

Mathematics

Probability

Scientific paper

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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