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

Large deviations for diffusions: Donsker and Varadhan meet Freidlin and Wentzell

“…the Donsker-Varadhan level two rate function for the occupation measure, has been achieved in [10]. The corresponding analysis for finite state Markov chains has been carried out in [5,23,24]. We emphasize that the limits as T → ∞ and ε → 0 do not commute for the higher order large deviations.…”

“…For these asymptotics, the order of the limit procedure ε → 0 and T → ∞ becomes relevant. We refer to [5,10,23,24] for the corresponding analysis in the context of reversible processes when the limit ε → 0 is taken after T → ∞.…”