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.
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Received: 31 December 1997 / Revised version: 14 April 1998
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Wüthrich, M. Scaling identity for crossing Brownian motion in a Poissonian potential. Probab Theory Relat Fields 112, 299–319 (1998). https://doi.org/10.1007/s004400050192
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DOI: https://doi.org/10.1007/s004400050192