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2011 Construction of a short path in high-dimensional first passage percolation
Olivier Couronné, Nathanaël Enriquez, Lucas Gerin
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Electron. Commun. Probab. 16: 22-28 (2011). DOI: 10.1214/ECP.v16-1595


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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Olivier Couronné. Nathanaël Enriquez. Lucas Gerin. "Construction of a short path in high-dimensional first passage percolation." Electron. Commun. Probab. 16 22 - 28, 2011.


Accepted: 9 January 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1231.60109
MathSciNet: MR2753301
Digital Object Identifier: 10.1214/ECP.v16-1595

Primary: 60K35
Secondary: 82B43

Keywords: first passage percolation , limit shape , Time constant

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