Upper large deviations for the maximal flow in first-passage percolation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:117

Article

Theret, Marie

关键词: first-passage percolation;    large deviations;    maximal flow;    max-flow min-cut;   

DOI  :  10.1016/j.spa.2006.12.007

来源: Elsevier

【 摘 要 】

We consider the standard first-passage percolation in Z(d) for d >= 2 and we denote by phi(d-1)(n),(h(n)) the maximal flow through the cylinder ]0,n](d-1) x]0, h(n)] from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension 3: under some assumptions, phi(d-1)(n),(h(n))/n(d-1) converges towards a constant v. We look now at the probability that phi(d-1)(n),(h(n))/n(d-1) is greater than v + 8 for some epsilon > 0, and we show under some assumptions that this probability decays exponentially fast with the volume n(d-1) h(n) of the cylinder. Moreover, we prove a large deviation principle for the sequence (phi(d-1)(n),(h(n))/n(d-1), n is an element of N). (C) 2007 Elsevier B.V. All rights reserved.

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