A Comparison Between Different Cycle Decompositions for Metropolis Dynamics

E.N.M. Cirillo, F.R. Nardi, J. Sohier

2016, v.22, Issue 3, 443-466


In the last decades the problem of metastability has been attacked on
rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper.
It is then useful to understand connections between different
point of views. In view of this
we consider irreducible, aperiodic and
reversible Markov chains with exponentially
small transition probabilities in the framework of Metropolis dynamics.
We compare two different cycle decompositions and prove their equivalence.

Keywords: stochastic dynamics, Markov chains, hitting times, Metropolis dynamics, metastability


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