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 $\xi \geq 3/5$.
@article{1022855742,
author = {W\"uthrich, Mario V.},
title = {Superdiffusive behavior of two-dimensional Brownian motion in a
Poissonian potential},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1000-1015},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855742}
}
Wüthrich, Mario V. Superdiffusive behavior of two-dimensional Brownian motion in a
Poissonian potential. Ann. Probab., Tome 26 (1998) no. 1, pp. 1000-1015. http://gdmltest.u-ga.fr/item/1022855742/