International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 803683, 43 pages
http://dx.doi.org/10.1155/2011/803683
Research Article

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

Xia Chen1 and Alexey Kulik2

1Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
2Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv 01601, Ukraine

Received 24 December 2010; Accepted 6 April 2011

Academic Editor: Nikolai Leonenko

Copyright © 2011 Xia Chen and Alexey Kulik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Schrödinger operators with their potential terms represented by renormalized Poisson potentials.