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October 1997 Critical large deviations of one-dimensional annealed Brownian motion in a Poissonian potential
Tobias Povel
Ann. Probab. 25(4): 1735-1773 (October 1997). DOI: 10.1214/aop/1023481109

Abstract

We derive a large deviation principle for the position at large times $t$ of a one-dimensional annealed Brownian motion in a Poissonian potential in the critical spatial scale $t^{1/3}$. Here “annealed” means that averages are taken with respect to both the path and environment measures. In contrast to the $d$-dimensional case for $d \geq 2$ in the critical scale $t^{d/(d+2)}$ as treated by Sznitman, the rate function which measures the large deviations exhibits three different regimes. These regimes depend on the position of the path at time $t$. Our large deviation principle has a natural application to the study of a one-dimensional annealed Brownian motion with a constant drift in a Poissonian potential.

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Tobias Povel. "Critical large deviations of one-dimensional annealed Brownian motion in a Poissonian potential." Ann. Probab. 25 (4) 1735 - 1773, October 1997. https://doi.org/10.1214/aop/1023481109

Information

Published: October 1997
First available in Project Euclid: 7 June 2002

zbMATH: 0911.60014
MathSciNet: MR1487434
Digital Object Identifier: 10.1214/aop/1023481109

Subjects:
Primary: 60F10, 82D30

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 4 • October 1997
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