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 …
Mixing of metastable diffusion processes with Gibbs invariant distribution
J Lee - arXiv preprint arXiv:2407.06383, 2024 - arxiv.org
In this article, we study the mixing properties of metastable diffusion processes which
possess a Gibbs invariant distribution. For systems with multiple stable equilibria, so-called …
possess a Gibbs invariant distribution. For systems with multiple stable equilibria, so-called …
Metastable Distributions for Semi-Markov Processes
IM Imtiyas - 2024 - search.proquest.com
In this work, we consider semi-Markov processes whose transition times and transition
probabilities depend on a small parameter ε. Understanding the asymptotic behavior of such …
probabilities depend on a small parameter ε. Understanding the asymptotic behavior of such …
Metastable hierarchy in abstract low-temperature lattice models: an application to Kawasaki dynamics for Ising lattice gas with macrscopic number of particles
S Kim - arXiv preprint arXiv:2405.08488, 2024 - arxiv.org
This article is divided into two parts. In the first part, we study the hierarchical phenomenon
of metastability in low-temperature lattice models in the most general setting. Given an …
of metastability in low-temperature lattice models in the most general setting. Given an …
A \emph{}-convergence of level-two large deviation for metastable systems: The case of zero-range processes
K Choi - arXiv preprint arXiv:2405.10631, 2024 - arxiv.org
This study explores the relationship between the precise asymptotics of the level-two large
deviation rate function and the behavior of metastable stochastic systems. Initially identified …
deviation rate function and the behavior of metastable stochastic systems. Initially identified …
Metastability of the three-state Potts model with asymmetrical external field
J Ahn - Stochastic Processes and their Applications, 2024 - Elsevier
In this paper, we explore the metastable behavior of the Glauber dynamics associated with
the three-state Potts model with an asymmetrical external field at a low-temperature regime …
the three-state Potts model with an asymmetrical external field at a low-temperature regime …
Metastable Distributions of Semi-Markov Processes
L Koralov, IM Imtiyas - arXiv preprint arXiv:2411.04795, 2024 - arxiv.org
In this paper, we consider semi-Markov processes whose transition times and transition
probabilities depend on a small parameter $\varepsilon $. Understanding the asymptotic …
probabilities depend on a small parameter $\varepsilon $. Understanding the asymptotic …
Metastability in Parabolic Equations and Diffusion Processes with a Small Parameter
M Freidlin, L Koralov - arXiv preprint arXiv:2403.12333, 2024 - arxiv.org
We study diffusion processes in $\mathbb {R}^ d $ that leave invariant a finite collection of
manifolds (surfaces or points) in $\mathbb {R}^ d $ and small perturbations of such …
manifolds (surfaces or points) in $\mathbb {R}^ d $ and small perturbations of such …
Metastability in Parabolic Equations and Diffusion Processes with a Small Parameter
L Koralov, M Freidlin - Available at SSRN 4948177 - papers.ssrn.com
We study diffusion processes in Rd that leave invariant a finite collection of manifolds in Rd.
Assuming certain ergodic properties at and near the invariant surfaces, we describe the rate …
Assuming certain ergodic properties at and near the invariant surfaces, we describe the rate …