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July 1998 Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential
Mario V. Wüthrich
Ann. Probab. 26(3): 1000-1015 (July 1998). DOI: 10.1214/aop/1022855742


We consider $d$-dimensional Brownian motion in a truncated Poissonian potential conditioned to reach a remote location. If Brownian motion starts at the origin and ends in an hyperplane at distance $L$ from the origin, the transverse fluctuation of the path is expected to be of order $L^{\xi}$ We are interested in a lower bound for $\xi$. We first show that $\xi \geq 1/2$ in dimensions $d \geq 2$ and then we prove superdiffusive behavior for $d = 2$, resulting in $\xi \geq 3/5$.


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Mario V. Wüthrich. "Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential." Ann. Probab. 26 (3) 1000 - 1015, July 1998.


Published: July 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0935.60099
MathSciNet: MR1634412
Digital Object Identifier: 10.1214/aop/1022855742

Primary: 60K35 , 82D30

Keywords: Brownian motion , Fluctuation , Poissonian potential , Superdiffusivity

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 3 • July 1998
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