Laurent Saloff-Coste

Learn More
. . ( ~ ) P ( X , Y )= T ( Y ) ~ ( Y , x) . By symmetry, P has eigenvalues 1= Po > P, 2 2 Pi,,-, 2 -1.This paper develops methods for getting upper and lower bounds on Pi by comparison with a second reversible chain on the same state space. This extends the ideas introduced in Diaconis and Saloff-Coste (1993), where random walks on finite groups were(More)
Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shuffling methods. From this viewpoint, one is interested in the “mixing time” of the chain, that is, the time at which the chain gives a good approximation of the limit(More)
Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Typical examples of such operators are the Laplace operators of Riemannian structures which are quasi-isometric to g . We first prove some Poincare and Sobolev(More)
We consider the problem of giving explicit spectral bounds for time inhomogeneous Markov chains on a finite state space. We give bounds that apply when there exists a probability π such that each of the different steps corresponds to a nice ergodic Markov kernel with stationary measure π . For instance, our results provide sharp bounds for models such as(More)
This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions of spectral gap and mixing time. Y. Peres has observed that for many families of Markov chains, there is a cutoff if and only if the product of spectral gap and(More)
Wreath products are a type of semidirect product. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return to the starting point of certain walks on wreath products is(More)