On the Hill relation and the mean reaction time for metastable processes

2020/08/22 by Manon Baudel, Baudel, Manon, Arnaud Guyader +3 · 1 citation
Physics and Astronomy · #60J22 #65C40 #82C31 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.2008.09790

openalex publication_date 2020/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We illustrate how the Hill relation and the notion of quasi-stationary distribution can be used to analyse the biasing error introduced by many numerical procedures that have been proposed in the literature, in particular in molecular dynamics, to compute mean reaction times between metastable states for Markov processes. The theoretical findings are illustrated on various examples demonstrating the sharpness of the biasing error analysis as well as the applicability of our study to elliptic diffusions.

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• Convergence, Sticking and Escape: Stochastic Dynamics Near Critical Points in SGD

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