Construction of a short path in high-dimensional first passage percolation

Olivier Couronné; Nathanaäl Enriquez; Lucas Gerin

doi:10.1214/ECP.v16-1595

Construction of a short path in high-dimensional first passage percolation

Olivier Couronné
, Nathanaäl Enriquez
, Lucas Gerin

Université Paris-Nanterre

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

Résumé

For first passage percolation in ℤ^d with large d, we construct a path connecting the origin to (x₁ = 1), whose passage time has optimal order log d/d. Besides, an improved lower bound for the “diagonal” speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidian ball in dimension larger than 35.

langue originale	Anglais
Pages (de - à)	22-28
Nombre de pages	7
journal	Electronic Communications in Probability
Volume	16
Les DOIs	https://doi.org/10.1214/ECP.v16-1595
état	Publié - 1 janv. 2011
Modification externe	Oui

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10.1214/ECP.v16-1595

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title = "Construction of a short path in high-dimensional first passage percolation",

abstract = "For first passage percolation in ℤd with large d, we construct a path connecting the origin to (x1 = 1), whose passage time has optimal order log d/d. Besides, an improved lower bound for the “diagonal” speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidian ball in dimension larger than 35.",

keywords = "First passage percolation, Limit shape, Time constant",

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AU - Couronné, Olivier

AU - Enriquez, Nathanaäl

AU - Gerin, Lucas

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N2 - For first passage percolation in ℤd with large d, we construct a path connecting the origin to (x1 = 1), whose passage time has optimal order log d/d. Besides, an improved lower bound for the “diagonal” speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidian ball in dimension larger than 35.

AB - For first passage percolation in ℤd with large d, we construct a path connecting the origin to (x1 = 1), whose passage time has optimal order log d/d. Besides, an improved lower bound for the “diagonal” speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidian ball in dimension larger than 35.

KW - First passage percolation

KW - Limit shape

KW - Time constant

U2 - 10.1214/ECP.v16-1595

DO - 10.1214/ECP.v16-1595

M3 - Article

AN - SCOPUS:79751469194

SN - 1083-589X

VL - 16

SP - 22

EP - 28

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Construction of a short path in high-dimensional first passage percolation

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