Brownian survival and Lifshitz tail in perturbed lattice disorder

In this talk, we consider the asymptotics for the survival probability of Brownian motion among randomly distributed traps. The configuration of traps is given by independent displacements of the lattice points, which gives a model of the Frenkel defects in a crystal. We determined both annealed and quenched asymptotics for the logarithm of the survival probability up to multiplicative constant. As applications, we show the Lifshitz tail effect of the density of states of associated random Schrödinger operator and intermittency in the parabolic problem.