On the length of one-dimensional reactive paths

Abstract : Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simplecsetting, namely paths generated by a one-dimensional overdamped Langevin equation for a double well potential. More precisely, we are interested in so-called reactive paths, namely trajectories which leave definitely one well and reach the other one. The aim of this paper is to precisely analyze the distribution of the lengths of reactive paths in the limit of small temperature, and to compare the theoretical results to numerical results obtained by a Monte Carlo method, namely the multi-level splitting approach.
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Contributor : Tony Lelièvre <>
Submitted on : Wednesday, June 6, 2012 - 10:00:07 AM
Last modification on : Friday, November 29, 2019 - 12:42:01 PM

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  • HAL Id : hal-00704704, version 1
  • ARXIV : 1206.0949


Frédéric Cérou, Arnaud Guyader, Tony Lelièvre, Florent Malrieu. On the length of one-dimensional reactive paths. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2013, 10 (1), pp.359-389. ⟨hal-00704704⟩



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