Brownian survival and Lifshitz tail in perturbed lattice disorder

Abstract

We consider the annealed asymptotics for the survival probability of Brownian motion among randomly distributed traps. The configuration of the traps is given by independent displacements of the lattice points. We determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant. As applications, we show the Lifshitz tail effect of the density of states of the associated random Schrödinger operator and derive a quantitative estimate for the strength of intermittency in the Parabolic Anderson problem.

arXiv comment24 pages, Major revision made for publication in J. Funct. Anal

References in corpus (1)

• Minimizing the ground state energy of an electron in a randomly deformed lattice

Cited by in corpus (8)

• Localization for the random displacement model
• Lifshitz tails for a class of Schrödinger operators with random breather-type potential
• Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
• Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential
• From the Lifshitz tail to the quenched survival asymptotics in the trapping problem
• Quenched tail estimate for the random walk in random scenery and in random layered conductance
• Quenched tail estimate for the random walk in random scenery and in random layered conductance II
• Low energy properties of the random displacement model