Mass concentration in the parabolic Anderson model
par
Renato dos Santos
→
Europe/Paris
Fokko du Cloux (La Doua, ICJ, Bât. Braconnier)
Fokko du Cloux
La Doua, ICJ, Bât. Braconnier
Description
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.