CONDITIONED, QUASI-STATIONARY, RESTRICTED MEASURES AND ESCAPE FROM METASTABLE STATES

We study the asymptotic hitting time tau((n)) of a family of Markov processes X-(n) to a target set G((n)) when the process starts from a "trap" defined by very general properties. We give an explicit description of the law of X-(n) conditioned to stay within the trap, and from this we deduce the exponential distribution of tau((n).) Our approach is very broad-it does not require reversibility, the target G does not need to be a rare event and the traps and the limit on n can be of very general nature-and leads to explicit bounds on the deviations of tau((n)) from exponentially. We provide two nontrivial examples to which our techniques directly apply.