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Lower bounds for point-to-point wandering exponents in Euclidean first-passage percolation

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  14 July 2016

C. Douglas Howard
C. Douglas Howard*
Affiliation:
The City University of New York
*
∗ Postal address: Mathematics Department, Baruch College, The City University of New York, 17 Lexington Ave., New York, NY 10010, USA. Email address: dhoward@baruch.cuny.edu
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Abstract

In first-passage percolation models, the passage time T(0,L) from the origin to a point L is expected to exhibit deviations of order |L|χ from its mean, while minimizing paths are expected to exhibit fluctuations of order |L|ξ away from the straight line segment . Here, for Euclidean models in dimension d, we establish the lower bounds ξ ≥ 1/(d+1) and χ ≥(1-(d-1)ξ)/2. Combining this latter bound with the known upper bound ξ ≤ 3/4 yields that χ ≥ 1/8 for d=2.

Keywords

Wandering exponentsEuclidean first-passage percolation

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82B43: Percolation 82B21: Continuum models (systems of particles, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1061 - 1073
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

Research supported in part by NSF Grant DMS-98-15226.

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