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1996 On the Non-Convexity of the Time Constant in First-Passage Percolation
Harry Kesten
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Electron. Commun. Probab. 1: 1-6 (1996). DOI: 10.1214/ECP.v1-971

Abstract

We give a counterexample to a conjecture of Hammersley and Welsh (1965) about the convexity of the time constant in first-passage percolation, as a functional on the space of distribution functions. The present counterexample only works for first-passage percolation on $Z^d$ for $d$ large.

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Harry Kesten. "On the Non-Convexity of the Time Constant in First-Passage Percolation." Electron. Commun. Probab. 1 1 - 6, 1996. https://doi.org/10.1214/ECP.v1-971

Information

Accepted: 25 January 1996; Published: 1996
First available in Project Euclid: 25 January 2016

zbMATH: 0866.60087
MathSciNet: MR1386288
Digital Object Identifier: 10.1214/ECP.v1-971

Subjects:
Primary: 60K35

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