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

Abstract We consider Fokker–Planck type differential operators associated with general
Langevin processes admitting a Gibbs stationary distribution. Under assumptions ensuring …

For many non-equilibrium dynamics driven by small noise, in physics, chemistry, biology, or
economy, rare events do matter. Large deviation theory then explains that the leading order …

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 article, we provide detailed analysis of the long-time behavior of the underdamped
Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise …

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 …

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 …