## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 3, 22-28.

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

https://projecteuclid.org/euclid.ecp/1465261959

Digital Object Identifier
doi:10.1214/ECP.v16-1595

Mathematical Reviews number (MathSciNet)
MR2753301

Zentralblatt MATH identifier
1231.60109

Rights