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math.PR2012★ 1 cited
A concentration theorem for the equilibrium measure of Markov chains with nonnegative coarse Ricci curvature
Laurent Veysseire
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. T…
math.PR2012★ 16 cited
Coarse Ricci curvature for continuous-time Markov processes
Laurent Veysseire
The coarse Ricci curvature for Markov chains is generalized for continuous time. We show that a positive coarse Ricci curvature implies a contraction of the Markov process for the…
math.PR2011★ 5 cited
Improved spectral gap bounds on positively curved manifolds
Laurent Veysseire
A coupling method and an analytic one allow us to prove new lower bounds for the spectral gap of reversible diffusions on compact manifolds. Those bounds are based on the a notion…