Distances in the highly supercritical percolation cluster

Anne Laure Basdevant; Nathanaël Enriquez; Lucas Gerin

doi:10.1214/12-AOP802

Distances in the highly supercritical percolation cluster

Anne Laure Basdevant
, Nathanaël Enriquez
, Lucas Gerin

Université Paris-Nanterre

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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-p/2 + 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).

Original language	English
Pages (from-to)	4342-4358
Number of pages	17
Journal	Annals of Probability
Volume	41
Issue number	6
DOIs	https://doi.org/10.1214/12-AOP802
Publication status	Published - 1 Nov 2013
Externally published	Yes

Keywords

First-passage percolation
Supercritical percolation
TASEP

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10.1214/12-AOP802

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title = "Distances in the highly supercritical percolation cluster",

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-p/2 + 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).",

keywords = "First-passage percolation, Supercritical percolation, TASEP",

author = "Basdevant, \{Anne Laure\} and Nathana{\"e}l Enriquez and Lucas Gerin",

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T1 - Distances in the highly supercritical percolation cluster

AU - Basdevant, Anne Laure

AU - Enriquez, Nathanaël

AU - Gerin, Lucas

PY - 2013/11/1

Y1 - 2013/11/1

N2 - 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-p/2 + 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).

AB - 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-p/2 + 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).

KW - First-passage percolation

KW - Supercritical percolation

KW - TASEP

U2 - 10.1214/12-AOP802

DO - 10.1214/12-AOP802

M3 - Article

AN - SCOPUS:84888422799

SN - 0091-1798

VL - 41

SP - 4342

EP - 4358

JO - Annals of Probability

JF - Annals of Probability

IS - 6

ER -

Distances in the highly supercritical percolation cluster

Abstract

Keywords

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