Tunnel effect for semiclassical random walk

speaker: Laurent Michel (Universite'de Nice)

abstract: We study natural random walks on Euclidean space endowed with a probability density. We investigate the convergence speed of such random walk towards its stationary distribution in semiclassical regime. The answer is given by estimates of the spectral gap of the associated Markov operator. We show that this gap is of order \(exp(-S/h)\), where h>0 is the semiclassical parameter used in the problem. The computation, of the constant S, involves study of tunnel effect in the spirit of works of Helffer-Sjöstrand and Helffer-Klein-Nier on Witten laplacian. One of the main ingredient of the proof, is to exhibit a super-symmetric structure for our operator.

timetable:
Tue 21 May, 9:00 - 9:50, Aula Dini
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