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We provide a necessary and sufficient condition for the metastability of a Markov chain, expressed in terms of a property of the solutions of the resolvent equation. As an application of this result, we prove the metastability of reversible, critical zero-range processes starting from a configuration.
In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of strong metastability time is introduced to describe the lo
A new expression as a certain asymptotic limit via discrete micro-states of permutations is provided to the mutual information of both continuous and discrete random variables.
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle with an op
It is well know that $SLE_kappa$ curves exhibit a phase transition at $kappa=4$. For $kappale 4$ they are simple curves with probability one, for $kappa>4$ they are not. The standard proof is based on the analysis of the Bessel SDE of dimension $d=1+
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching process c