A concentration theorem for the equilibrium measure of Markov chains   with nonnegative coarse Ricci curvature
  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. 
Laurent Veysseire (UMPA-ENSL)
math.PR