|Sep 08, 2022
|University of Helsinki
온라인 (Zoom) 세미나; Zoom 주소 937 905 874
Abstract: In this talk, I will study the so-called cutoff phenomenon for the Langevin dynamics with a strongly coercive potential and driven by an additive noise with small amplitude. When the driven noise is the Brownian motion, I will show that the total variation distance between the current state and its equilibrium distribution decays around the mixing time from its maximum to zero abruptly. This is known in the literature as the cutoff phenomenon introduced in the context of card shuffling. When the noise is alpha-stable or more general Layered stable with index alpha>3/2, cutoff phenomenon still holds whereas for alphaleq 3/2 the coupling techniques do not apply and hence we cannot conclude if the cutoff phenomenon still holds.
The talk is based on series of papers with Milton Jara (IMPA, Brazil), Michael Högele (Universidad de los Andes, Colombia) and Juan Carlos Pardo (CIMAT, Mexico).