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We consider the exit event from a metastable state for the overdamped Langevin dynamics $$dX_t = -\nabla f(X_t) dt + \sqrt{h} dB_t$$ dXt=-∇f(Xt)dt+hdBt . Using tools from semiclassical analysis, we prove that, starting from the quasi stationary distribution within the state, the exit event can be modeled using a jump Markov process parametrized with the Eyring–Kramers formula, in the small temperature...
Accurate asymptotic expressions are given for the exponentially small eigenvalues of Witten Laplacians acting on p-forms. The key ingredient, which replaces explicit formulas for global quasimodes in the case p = 0, is Barannikov’s presentation of Morse theory in Barannikov (Adv Soviet Math 21:93–115, 1994).
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