Mass concentration in the parabolic Anderson model

par Renato dos Santos

jeudi 2 févr. 2017, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (La Doua, ICJ, Bât. Braconnier)

We consider the positive solution of the heat equation with random potential on the d-dimensional lattice with initial condition localised at the origin. The potential is supposed i.i.d. with upper tails close to doubly-exponential. In this case, the solution is known to exhibit intermittent behaviour, i.e., its mass is asymptotically concentrated on relatively small ``islands'' that are well-separated in space. The number of islands needed is known to be a.s. asymptotically bounded by any small power of time. We show that, with probability tending to one as time increases, most of the mass of the solution is carried by a single island whose size remains bounded. Joint work with Marek Biskup and Wolfgang Koenig.