METASTABILITY OF EXPONENTIALLY PERTURBED MARKOV-CHAINS

A family of irreducible Markov chains on a finite state space is consi dered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by stu dies of stochastic Ising models, neural network and simulated annealin g. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those re current states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are e stimated. The hitting time over its mean converges in law to the unit exponential distribution.