亚稳态的出射：低能鞍点上出射点分布的集中，第2部分
The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points, part 2
摘要：
在对$f$相当一般的假设下（例如，在$Ω$中$f$可能有多个临界点），考虑了从$Ω$中确定性初始条件出发的随机过程$(X_t)_{t\ge 0}$解到过阻尼Langevin动力学$$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t$$的有界域$Ω$的第一出口点分布.这项工作是前一篇论文\cite{DLLN-saddle1}的继续，其中$Ω$的出口点分布进行了研究时，$X_0$最初分布根据准平稳分布的$(X_t)_{t\ge 0}$在$Ω$。证明基于出口点分布对初始条件的依赖性的分析结果、大偏差技术和莫尔斯函数的通用性结果。
英文摘要：
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.
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