Annealed Brownian motion in a heavy tailed Poissonian potential
arXiv:1107.2315 · doi:10.1214/12-AOP754
Abstract
Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative 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.
Published in at http://dx.doi.org/10.1214/12-AOP754 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)