Scaling identity for crossing Brownian motion in a Poissonian potential

被引：0
|
作者：
Mario V. Wüthrich
机构：
[1] Department of Mathematics,
[2] ETH Zentrum,undefined
[3] HG G47.1,undefined
[4] CH-8092 Zürich,undefined
[5] Switzerland. e-mail: mwueth@math.ethz.ch,undefined
来源：
Probability Theory and Related Fields | 1998年 / 112卷
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Mathematics Subject Classification (1991): 60K35; 82D30;
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学科分类号：
摘要：
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.
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页码：299 / 319
页数：20
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