Séminaire Orléans

Metastable dynamics of perturbed Markov Chains
Volker Betz (Darmstadt)
Thursday 21 May 2015 14:00 -  Orléans -  Salle de Séminaire

Résumé :
We consider a family of Markov chains whose transition matrix depends continuously on a small parameter $\epsilon$ and is such that the chain is irreducible for $\epsilon > 0$ but has several essential classes for $\epsilon = 0$. This leads to multi-scale metastable dynamical behavior of the chain. We present a systematic approach, based on potential theory, that recursively coarse-grains the state space in order to resolve the dynamics on the different timescales. As a by-product of this procedure, we give an efficient algorithm for computing the asymptotic stationary distribution of the chain. The main advance over the existing approaches based on potential theory is that we do not require the chains to be reversible.

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