28/09/2022, 17:00 — 18:00 — Online
Claudio Landim, IMPA-Brasil
Metastability from the point of view of large deviations
Consider a sequence of continuous-time Markov chains $X^n_t$ evolving on a fixed finite state space $V$. Let $I_n$ be its level two large deviations rate functiona. Under a general hypothesis on the jump rates, we derive an expansion for $I_n$: we show that $I_n$ can be written as$ I^0 + \sum_{1\ le p\le q} (\theta^p_n)^{-1} I^p$ In this formula, $\theta^p_n$ are the time-scales at which a meta-stable behavior is observed and I^p the level two large deviations rate function of the Markov chain which describes the evolution of the chain $X^n_t$ in the time-scale $\theta^p_n$.
