The shape of large balls in highly supercritical percolation

Anne Laure Basdevant; Nathanaël Enriquez; Lucas Geriny; Jean Baptiste Gouéréz

doi:10.1214/EJP.v19-3062

The shape of large balls in highly supercritical percolation

Anne Laure Basdevant
, Nathanaël Enriquez
, Lucas Geriny
, Jean Baptiste Gouéréz

Université Paris-Nanterre
conventionnée avec l'Université d'Orléans

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

Abstract

We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on ℤ. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.

Original language	English
Article number	26
Journal	Electronic Journal of Probability
Volume	19
DOIs	https://doi.org/10.1214/EJP.v19-3062
Publication status	Published - 28 Feb 2014

Keywords

First-passage percolation
Supercritical percolation
TASEP

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10.1214/EJP.v19-3062

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title = "The shape of large balls in highly supercritical percolation",

abstract = "We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on ℤ. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.",

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

author = "Basdevant, \{Anne Laure\} and Nathana{\"e}l Enriquez and Lucas Geriny and Gou{\'e}r{\'e}z, \{Jean Baptiste\}",

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AU - Basdevant, Anne Laure

AU - Enriquez, Nathanaël

AU - Geriny, Lucas

AU - Gouéréz, Jean Baptiste

PY - 2014/2/28

Y1 - 2014/2/28

N2 - We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on ℤ. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.

AB - We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on ℤ. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.

KW - First-passage percolation

KW - Supercritical percolation

KW - TASEP

U2 - 10.1214/EJP.v19-3062

DO - 10.1214/EJP.v19-3062

M3 - Article

AN - SCOPUS:84897807443

SN - 1083-6489

VL - 19

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 26

ER -

The shape of large balls in highly supercritical percolation

Abstract

Keywords

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