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September 2013 Annealed Brownian motion in a heavy tailed Poissonian potential
Ryoki Fukushima
Ann. Probab. 41(5): 3462-3493 (September 2013). 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.

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Ryoki Fukushima. "Annealed Brownian motion in a heavy tailed Poissonian potential." Ann. Probab. 41 (5) 3462 - 3493, September 2013. https://doi.org/10.1214/12-AOP754

Information

Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1279.60127
MathSciNet: MR3127888
Digital Object Identifier: 10.1214/12-AOP754

Subjects:
Primary: 60K37
Secondary: 82B44

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 5 • September 2013
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