Annealed Brownian motion in a heavy tailed Poissonian potential
Probability
2013-10-04 v3
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.
Keywords
Cite
@article{arxiv.1107.2315,
title = {Annealed Brownian motion in a heavy tailed Poissonian potential},
author = {Ryoki Fukushima},
journal= {arXiv preprint arXiv:1107.2315},
year = {2013}
}
Comments
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)