Scaling identity for crossing Brownian motion in a Poissonian potential |
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Authors: | Mario V Wüthrich |
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Institution: | (1) Department of Mathematics, ETH Zentrum, HG G47.1, CH-8092 Zürich, Switzerland. e-mail: mwueth@math.ethz.ch, CH |
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Abstract: | We consider d-dimensional Brownian motion in a truncated Poissonian potential (d≥ 2). If Brownian motion starts at the origin and ends in the closed ball with center y and radius 1, then the transverse fluctuation of the path is expected to be of order |y|ξ, whereas the distance fluctuation is of order |y|χ. Physics literature tells us that ξ and χ should satisfy a scaling identity 2ξ− 1 = χ. We give here rigorous results for
this conjecture.
Received: 31 December 1997 / Revised version: 14 April 1998 |
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Keywords: | Mathematics Subject Classification (1991): 60K35 82D30 |
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