论文标题
从亚稳态状态的退出：低能鞍点上出口点分布的浓度，第2部分
The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points, part 2
论文作者
论文摘要
我们考虑从有界域$ω$的第一个退出点分布，$（x_t）_ {t \ ge 0} $解决方案到过度抑制了langevin dynamics $$ d x_t = - \ nabla f（x_t）d t t t t t t t t t + \ sqrt { $ f $（例如，$ f $在$ω$中可能有几个关键点）。这项工作是以前的论文\ cite {dlln-saddle1}的延续，其中当$ x_0 $根据$（x_t）_ {t \ ge 0} $ in $ω$的准平台分布最初分配$ x_0 $时，研究了$ω$的出口分布。证明基于对出口点分布对初始条件的依赖性的分析结果，较大的偏差技术以及对摩尔斯函数的通用性的结果。
We consider the first exit point distribution from a bounded domain $Ω$ of the stochastic process $(X_t)_{t\ge 0}$ solution to the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t$$ starting from deterministic initial conditions in $Ω$, under rather general assumptions on $f$ (for instance, $f$ may have several critical points in $Ω$). This work is a continuation of the previous paper \cite{DLLN-saddle1} where the exit point distribution from $Ω$ is studied when $X_0$ is initially distributed according to the quasi-stationary distribution of $(X_t)_{t\ge 0}$ in $Ω$. 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.
