Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential

The parabolic Anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied. The moment asymptotics of the total mass of the solution is derived. The results show that the total mass of the solution concentrates on a small set in the space of configuration. © 2010 Elsevier Inc. All rights reserved.