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 …
We consider small perturbations of a dynamical system on the one-dimensional torus. We derive sharp estimates for the pre-factor of the stationary state, we examine the asymptotic …
C Oh, F Rezakhanlou - preprint, 2019 - math.berkeley.edu
We prove the metastability of zero range processes on a finite set with an approach using the Poisson equation. Certain zero range processes on a finite set exhibit condensation …
We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied …
We prove that the position of the condensate of reversible, critical zero-range processes on a finite set S evolves, in a suitable time scale, as a continuous-time Markov chain on S …
We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+ 1 scales (ie N small scales and one macroscale) and to depend periodically on …
I Seo - arXiv preprint arXiv:1905.00743, 2019 - arxiv.org
We herein review the recent progress on the study of metastability based on the analysis of solutions of Poisson equations related to the generators of the underlying metastable …
C Landim - arXiv preprint arXiv:1712.03528, 2017 - arxiv.org
arXiv:1712.03528v1 [math.PR] 10 Dec 2017 Page 1 arXiv:1712.03528v1 [math.PR] 10 Dec 2017 VARIATIONAL FORMULAE FOR THE CAPACITY INDUCED BY SECOND-ORDER …