The Annals of Probability

On the chemical distance for supercritical Bernoulli percolation

Peter Antal and Agoston Pisztora

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 11 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039639377

Digital Object Identifier
doi:10.1214/aop/1039639377

Mathematical Reviews number (MathSciNet)
MR1404543

Zentralblatt MATH identifier
0871.60089

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

Keywords
Graph distance percolation supercritical phase large deviations

Citation

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. https://projecteuclid.org/euclid.aop/1039639377


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References

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