Phase transitions and metastability in Markovian and molecular systems
The purpose of this paper is to develop foundations for model reduction and new modeling techniques for diffusion models. These foundations are all based upon the recent spectral theory of Markov process. The main assumption imposed is V-uniform ergodicity of the process. Under this assumption the authors show that the associated semigroup admits a spectral gap in a weighted \(L_{\infty}\)-norm and real eigenfunctions provide a decomposition of the state space into ``almost''-absorbing subsets. The authors also show that the process mixes rapidly in each of these subsets prior to existing and that the conditional distributions of exit times are approximately exponential. These results represent a significant expansion of the classical Wentzell-Freidlin theory.
scientific article; zbMATH DE number 2072704
scientific article