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

Olivier Couronné (Universite Paris-Ouest)
Nathanaël Enriquez (Universite Paris-Ouest)
Lucas Gerin (Universite Paris-Ouest)

Abstract


For first passage percolation in $\mathbb{Z}^d$ with large $d$, we construct a path connecting the origin to $\{x_1 =1\}$, 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 euclidean ball in dimension larger than 35.

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Pages: 22-28

Publication Date: January 9, 2011

DOI: 10.1214/ECP.v16-1595

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