Consider a probability measure μ supported by a regular geodesic ball in a manifold. For any p≥1 we define a stochastic algorithm which converges almost surely to the p-mean ep of μ. Assuming furthermore that the functional to minimize is regular around ep, we prove that a natural...

A gradient-entropy inequality is established for elliptic diffusion semigroups on arbitrary complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived.

We prove Cheng-Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an...

Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min–max or max–min Dirichlet connectivity criteria are investigated. Links...

Let (L[theta])[theta][epsilon]N be a family of elliptic diffusion operators on a compact and connected smooth manifold M, whose terms of first order are indexed by a parameter [theta] living in N, the n-dimensional torus. For each fixed [theta], we associate to L[theta] its invariant probability...

We consider the simulated annealing algorithm associated to a potential U on a graph (M, q) (reversible or satisfying the Hajek's weak reversibility condition), whose temperature at time t [greater-or-equal, slanted] 0 is given by k ln-1 (1 + t), with k c(M, U) the critical constant for the...