Cover time for the random walk and Brownian motion on the two-dimensional torus and random interlacement (Francis Comets, University of Paris 7, France)

03.04.2017 15:15 – 17:15

The cover time is the time needed to visit all points on the lattice, and in the continuum, for the Wiener sausage of radius 1 to cover the torus of linear size n. As a maximum of correlated random variables (here, with logarithmic decay) it has interesting asymptotics. In higher dimension random interlacements, introduced by Sznitman to describe the local covering picture with a fixed intensity, still give a reliable account at large densities up to cover time. In dimension 2, it can be used as a description of the neighborhood of an unvisited site, provided that the paths used in the interlacement are random walk and Brownian motion conditioned not to visit a ball. (Joint works with Serguei Popov and Marina Vachkovskaia.)

Lieu

Room 17 15:15-16:00 & Room 17 16:30-17:15, Séminaire "Mathématique Physique"

entrée libre