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