We study a large class of reversible Markov chains with discrete state space and transition matrix PN . We define the notion of a set of metastable points as a subset of the state space Î“N such thatâ€¦ (More)

We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form âˆ’ 1+âˆ‡F(Â·)âˆ‡ onRd or subsets of Rd , whereF is a smooth functionâ€¦ (More)

We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that weâ€¦ (More)

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of theâ€¦ (More)

This is the first of a series of three papers in which we present a full rigorous analysis of a class of spin glass models in by Derrida under the name of Generalised Random Energy Models (GREM).â€¦ (More)

We prove that the extremal process of branching Brownian motion, in the limit of large times, converges weakly to a cluster point process. The limiting process is a (randomly shifted) Poisson clusterâ€¦ (More)

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean eld models at low temperatures. Our main purpose is to give a precise relationâ€¦ (More)

We investigate one-dimensional discrete Schrr odinger operators whose potentials are invariant under a substitution rule. The spectral properties of these operators can be obtained from the analysisâ€¦ (More)

In this paper we study the metastable behavior of one of the simplest disordered spin system, the random field Curie-Weiss model. We will show how the potential theoretic approach can be used toâ€¦ (More)