Title: Precise estimates on noise-induced transitions between oscillating double-well potentials

Abstract: We consider stochastic differential equations describing the motion of an overdamped Brownian particle in a periodically oscillating double-well potential. Our main objective is to describe the distribution of transition times between potential wells. Without periodic perturbation, the answer to this question is well known: the distribution of transition times is asymptotically exponential, with an expectation given by the so-called Eyring-Kramers law. With the periodic perturbation, the equation becomes non-reversible, which makes the analysis much harder. We will present results both on the shape of the distribution of transition times, and on its expectation for a range of oscillation frequencies. Partly based on joint work with Barbara Gentz (Bielefeld).

 

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