Second order asymptotics for Brownian motion in a heavy tailed Poissonian potential

Details Second order asymptotics for Brownian motion in a heavy tailed Poissonian potential Second order asymptotics for Brownian motion in a heavy tailed Poissonian potential

2010-10-19

arxiv.org/abs/1010.3875v3

Markov Processes and Related Fields 2011, Volume 17, Issue 3, 447-482

Mathematics

Probability

29 pages. Minor corrections

Scientific paper

We consider the Feynman-Kac functional associated with a Brownian motion in a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by Pastur (1977) and the first order term of the moment asymptotics was determined. In this paper, both moment and almost sure asymptotics are determined up to the second order. As an application, we also derive the second order asymptotics of the integrated density of states of the corresponding random Schr\"odinger operator.

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