Asymptotics of Negative Exponential Moments for Annealed Brownian Motion in a Renormalized Poisson Potential

Abstract

In (Chen and Kulik, 2009), a method of renormalization was proposed for constructing some more physically realistic random potentials in a Poisson cloud. This paper is devoted to the detailed analysis of the asymptotic behavior of the annealed negative exponential moments for the Brownian motion in a renormalized Poisson potential. The main results of the paper are applied to studying the Lifshitz tails asymptotics of the integrated density of states for random Schrodinger operators with their potential terms represented by renormalized Poisson potentials.