The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points, part 2

We consider the first exit point distribution from a bounded domain Omega of the stochastic process (X-t)(t >= 0) solution to the overdamped Langevin dynamics dX(t) = -del f(X-t)dt + root h dB(t) starting from deterministic initial conditions in Omega, under rather general assumptions on f (for instance, f may have several critical points in Omega). This work is a continuation of the previous paper [14] where the exit point distribution from Omega is studied when X-0 is initially distributed according to the quasi-stationary distribution of (X-t)(t >= 0) in Omega. The proofs are based on analytical results on the dependency of the exit point distribution on the initial condition, large deviation techniques and results on the genericity of Morse functions.

Automated summary

This work examines the exit point distribution from a bounded domain of a stochastic process, taking into account the influence of initial conditions on the distribution. The proofs rely on analytical results on the dependency of the exit point distribution on the initial condition, as well as large deviation techniques and results on the genericity of Morse functions.