论文标题
从大偏差的角度来看：$γ$ - 二级大偏差率的非可逆性有限状态马尔可夫链的功能
Metastability from the large deviations point of view: A $Γ$-expansion of the level two large deviations rate functional of non-reversible finite-state Markov chains
论文作者
论文摘要
考虑一系列连续的时间马尔可夫链$（x^{（n）} _ t：t \ ge 0）$在固定有限状态空间$ v $上演变。令$ i_n $为$ x^{（n）} _ t $的第二级大偏差率，为$ t \ to \ infty $。根据关于跳高速率的假设，我们证明$ i_n $可以写入$ i_n = i^{（0）} \，+\，\ sum_ {1 \ le p \ le p \ le q}（1/θ^{（p）_ n）\，I^（p）\，I^（p）{（p）{（p）{（p）{（p）} $。权重$θ^{（p）} _ n $对应于马尔可夫链序列$ x^{（n）} _ t $表现出亚稳态行为的时间表，而速率函数的零级集$ i^{（p）} $ neverable的行为。
Consider a sequence of continuous-time Markov chains $(X^{(n)}_t:t\ge 0)$ evolving on a fixed finite state space $V$. Let $I_n$ be the level two large deviations rate functional for $X^{(n)}_t$, as $t\to\infty$. Under a hypothesis on the jump rates, we prove that $I_n$ can be written as $I_n = I^{(0)} \,+\, \sum_{1\le p\le q} (1/θ^{(p)}_n) \, I^{(p)}$ for some rate functionals $I^{(p)}$. The weights $θ^{(p)}_n$ correspond to the time-scales at which the sequence of Markov chains $X^{(n)}_t$ exhibit a metastable behavior, and the zero level sets of the rate functionals $I^{(p)}$ identify the metastable states.
