Annealed Brownian motion in a heavy tailed Poissonian potential

Details Annealed Brownian motion in a heavy tailed Poissonian potential Annealed Brownian motion in a heavy tailed Poissonian potential

2011-07-12

arxiv.org/abs/1107.2315v2

Mathematics

Probability

32 pages, minor corrections

Scientific paper

Consider a $d$-dimensional Brownian motion in a random potential defined by attaching a non-negative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson points by weighting the measure by the Feynman-Kac functional. We show that under the weighted measure, the Brownian motion tends to localize around the origin. We also determine the scaling limit of the path and also the limit shape of the random potential.

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