Distances in the highly supercritical percolation cluster

Authors
Basdevant, Anne-Laure Enriquez, Nathanaël Gerin, Lucas
Citation
Basdevant, Anne-laure et al., Distances in the highly supercritical percolation cluster, Annals of probability , 41(6), 2013, pp. 4342-4358
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
41
Issue
6
Year of publication
2013
Pages
4342 - 4358
Database
ACNP
SICI code
Abstract
On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1+1.p2+o(1.p) with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).