Consider the elliptic operator given by 0.1 L ε f= b·∇ f+ ε Δ f for some smooth vector field b: R
d→ R d and a small parameter ε> 0. Consider the initial-valued problem 0.2∂ tu ε= L ε u ε, u …

In this article, we perform quantitative analyses of metastable behavior of an interacting
particle system known as the inclusion process. For inclusion processes, it is widely …

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 …

In this article, we study the hierarchical structure of metastability in the reversible inclusion
process. We fully characterize the third time scale of metastability subject to any underlying …

In this article, we prove the Eyring–Kramers formula for non-reversible metastable diffusion
processes that have a Gibbs invariant measure. Our result indicates that non-reversible …

Consider a sequence of continuous-time Markov chains (X t (n): t≥ 0) evolving on a fixed
finite state space V. Let I n be the level two large deviations rate functional for X t (n), as …

We examine two analytical characterisation of the metastable behavior of a Markov chain.
The first one expressed in terms of its transition probabilities, and the second one in terms of …

The main contribution of the current study is two-fold. First, we investigate the energy
landscape of the Ising and Potts models on finite two-dimensional lattices without external …

In this study, we investigate the metastable behavior of Metropolis-type Glauber dynamics
associated with the Blume–Capel model with zero chemical potential and zero external field …

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 …