## Annals of Probability

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

Ryoki Fukushima

#### 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.

#### Article information

Source
Ann. Probab., Volume 41, Number 5 (2013), 3462-3493.

Dates
First available in Project Euclid: 12 September 2013

https://projecteuclid.org/euclid.aop/1378991845

Digital Object Identifier
doi:10.1214/12-AOP754

Mathematical Reviews number (MathSciNet)
MR3127888

Zentralblatt MATH identifier
1279.60127

#### Citation

Fukushima, Ryoki. Annealed Brownian motion in a heavy tailed Poissonian potential. Ann. Probab. 41 (2013), no. 5, 3462--3493. doi:10.1214/12-AOP754. https://projecteuclid.org/euclid.aop/1378991845

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