The Annals of Probability

On the chemical distance for supercritical Bernoulli percolation

Peter Antal and Agoston Pisztora

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We prove large deviation estimates at the correct order for the graph distance of two sites lying in the same cluster of an independent percolation process. We improve earlier results of Gärtner and Molchanov and Grimmett and Marstrand and answer affirmatively a conjecture of Kozlov.

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Ann. Probab., Volume 24, Number 2 (1996), 1036-1048.

First available in Project Euclid: 11 December 2002

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35]

Graph distance percolation supercritical phase large deviations


Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996), no. 2, 1036--1048. doi:10.1214/aop/1039639377.

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