Generalized Langevin And Nosé-hoover Processes Absorbed At The Boundary Of A Metastable Domain

2024/03/26 by Arnaud Guillin, Dawei Lu, Guillin, Arnaud +5
Economics, Econometrics and Finance · Mathematics · #Boundary (topology) #Domain (mathematical analysis) #FOS: Mathematics #Langevin dynamics #Langevin equation #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Metastability #Physics #Probability (math.PR) #Quantum mechanics #Statistical physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2403.17471

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential conver- gence towards the quasi-stationary distribution for the generalized Langevin and the Nosé-Hoover processes, two processes which are widely used in molecular dynamics. The case of singular potentials is considered. With the techniques used in this work, we are also able to greatly improve existing results on quasi-stationary distributions for the kinetic Langevin process to a weak regularity setting.

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