Numerical bounds for critical exponents of crossing Brownian motion
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- by Mario V. Wüthrich PDF
- Proc. Amer. Math. Soc. 130 (2002), 217-225 Request permission
Abstract:
We consider $d$-dimensional crossing Brownian motion in a truncated Poissonian potential conditioned to reach a fixed hyperplane at distance $L$ from the starting point. The transverse fluctuation of the path is expected to be of order $L^\xi$. We prove that for $d\ge 2$: $\xi \le 3/4$. As a second critical exponent we introduce $\chi ^{(2)}$, which describes the fluctuations of naturally defined distance functions for crossing Brownian motion. The numerical bound we obtain is an improvement of Corollary 3.1 in Scaling identity for crossing Brownian motion in a Poissonian potential (Probab. Theory Related Fields 112 (1998), 299–319), resulting in $\chi ^{(2)} \ge 1/5$ if $d=2$ and if the killing rate $\lambda$ is strictly positive ($\lambda >0$).References
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Additional Information
- Mario V. Wüthrich
- Affiliation: Department of Mathematics, University of Nijmegen, Toernooiveld 1, NL-6525 ED Nijmegen, The Netherlands
- Address at time of publication: Winterthur Insurance, Roemerstrasse 17, P.O. Box 357, CH-8401 Winterthur, Switzerland
- Email: mario.wuethrich@winterthur.ch
- Received by editor(s): September 1, 1999
- Received by editor(s) in revised form: May 24, 2000
- Published electronically: May 22, 2001
- Communicated by: Claudia M. Neuhauser
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 217-225
- MSC (2000): Primary 60K35, 82D30
- DOI: https://doi.org/10.1090/S0002-9939-01-06017-8
- MathSciNet review: 1855632