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Scaling identity for crossing Brownian motion in a Poissonian potential
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  • Published: November 1998

Scaling identity for crossing Brownian motion in a Poissonian potential

  • Mario V. Wüthrich1 

Probability Theory and Related Fields volume 112, pages 299–319 (1998)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics, ETH Zentrum, HG G47.1, CH-8092 Zürich, Switzerland. e-mail: mwueth@math.ethz.ch, , , , , , CH

    Mario V. Wüthrich

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  1. Mario V. Wüthrich
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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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  • Issue Date: November 1998

  • DOI: https://doi.org/10.1007/s004400050192

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  • Mathematics Subject Classification (1991): 60K35
  • 82D30
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