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The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points, part 2
Abstract : We consider the first exit point distribution from a bounded domain $\Omega$ of the stochastic process $(X_t)_{t\ge 0}$ solution to the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t$$ 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 \cite{DLLN-saddle1} where the exit point distribution from $\Omega$ is studied when $X_0$ is initially distributed according to the
quasi-stationary distribution of $(X_t)_{t\ge 0}$ 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.
https://hal.archives-ouvertes.fr/hal-03058529
Contributor : Dorian Le Peutrec <>
Submitted on : Friday, December 11, 2020 - 6:40:58 PM
Last modification on : Friday, January 15, 2021 - 5:52:47 PM
Contributor : Dorian Le Peutrec <>
Submitted on : Friday, December 11, 2020 - 6:40:58 PM
Last modification on : Friday, January 15, 2021 - 5:52:47 PM
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