Electronic Communications in Probability

Strict Convexity of the Limit Shape in First-Passage Percolation

Steven Lalley

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Sufficient conditions are given for the strict convexity of the limit shape in standard first-passage percolation. These conditions involve (1) asymptotic ``straightness'' of the geodesics, and (2) existence of mean-zero limit distributions for the first-passage times.

Article information

Electron. Commun. Probab., Volume 8 (2003), paper no. 15, 135-141.

Accepted: 7 November 2003
First available in Project Euclid: 18 May 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

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Lalley, Steven. Strict Convexity of the Limit Shape in First-Passage Percolation. Electron. Commun. Probab. 8 (2003), paper no. 15, 135--141. doi:10.1214/ECP.v8-1089. https://projecteuclid.org/euclid.ecp/1463608899

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