Section: New Results

On the length of one–dimensional reactive paths

Participants : Frédéric Cérou, Arnaud Guyader, Florent Malrieu.

See  3.3 and  4.2 .

This is a collaboration with Tony Lelièvre (ENPC).

Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simple setting, 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 [32] 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.