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.
Publié le : 1996-04-14
Classification:
Graph distance,
percolation,
supercritical phase,
large deviations,
60K35,
82B43
@article{1039639377,
author = {Antal, Peter and Pisztora, Agoston},
title = {On the chemical distance for supercritical Bernoulli
percolation},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1036-1048},
language = {en},
url = {http://dml.mathdoc.fr/item/1039639377}
}
Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli
percolation. Ann. Probab., Tome 24 (1996) no. 2, pp. 1036-1048. http://gdmltest.u-ga.fr/item/1039639377/