A resolvent approach to metastability
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 …
expressed in terms of a property of the solutions of the resolvent equation. As an application …
Energy landscape and metastability of stochastic Ising and Potts models on three-dimensional lattices without external fields
In this study, we investigate the energy landscape of the Ising and Potts models on fixed and
finite but large three-dimensional (3D) lattices where no external field exists and …
finite but large three-dimensional (3D) lattices where no external field exists and …
Non-reversible metastable diffusions with Gibbs invariant measure II: Markov chain convergence
This article considers a class of metastable non-reversible diffusion processes whose
invariant measure is a Gibbs measure associated with a Morse potential. In a companion …
invariant measure is a Gibbs measure associated with a Morse potential. In a companion …
Scaling limit of small random perturbation of dynamical systems
F Rezakhanlou, I Seo - arXiv preprint arXiv:1812.02069, 2018 - arxiv.org
In this article, we prove that a small random perturbation of dynamical system with multiple
stable equilibria converges to a Markov chain whose states are neighborhoods of the …
stable equilibria converges to a Markov chain whose states are neighborhoods of the …
Metastable behavior of weakly mixing Markov chains: the case of reversible, critical zero-range processes
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 …
chains. This approach is based on properties of the resolvent equations and can be applied …
Generalized Dirichlet and Thomson Principles and Their Applications
I Seo - arXiv preprint arXiv:2102.05538, 2021 - arxiv.org
arXiv:2102.05538v1 [math.PR] 10 Feb 2021 Page 1 GENERALIZED DIRICHLET AND
THOMSON PRINCIPLES AND THEIR APPLICATIONS INSUK SEO Contents Introduction 2 …
THOMSON PRINCIPLES AND THEIR APPLICATIONS INSUK SEO Contents Introduction 2 …
Condensation of the invariant measures of the supercritical zero range processes
T Xu - arXiv preprint arXiv:2007.06085, 2020 - arxiv.org
For $\alpha\geq 1$, let $ g:\mathbb N\to\mathbb R_+ $ be given by $ g (0)= 0$, $ g (1)= 1$, $
g (k)=(k/k-1)^\alpha $, $ k\geq 2$. Consider the symmetric nearest neighbour zero range …
g (k)=(k/k-1)^\alpha $, $ k\geq 2$. Consider the symmetric nearest neighbour zero range …