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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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).

langue originale	Anglais
Pages (de - à)	4342-4358
Nombre de pages	17
journal	Annals of Probability
Volume	41
Numéro de publication	6
Les DOIs	https://doi.org/10.1214/12-AOP802
état	Publié - 1 nov. 2013
Modification externe	Oui

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10.1214/12-AOP802

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@article{0fa80a8c3e334cd08e933de0ebe05e33,

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",

year = "2013",

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day = "1",

doi = "10.1214/12-AOP802",

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TY - JOUR

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

Résumé

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