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October, 1995 Asymptotic Shapes for Stationary First Passage Percolation
Olle Haggstrom, Ronald Meester
Ann. Probab. 23(4): 1511-1522 (October, 1995). DOI: 10.1214/aop/1176987792

Abstract

This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well known asymptotic shape result is known to extend to this case. It is easy to give necessary conditions for a compact set $B \subset \mathbb{R}^d$ to arise as the asymptotic shape for some stationary measure on the passage times. Our main result says that these conditions are also sufficient.

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Olle Haggstrom. Ronald Meester. "Asymptotic Shapes for Stationary First Passage Percolation." Ann. Probab. 23 (4) 1511 - 1522, October, 1995. https://doi.org/10.1214/aop/1176987792

Information

Published: October, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0852.60104
MathSciNet: MR1379157
Digital Object Identifier: 10.1214/aop/1176987792

Subjects:
Primary: 60K35

Keywords: asymptotic shape , first passage percolation , subadditivity‎

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 4 • October, 1995
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