Electronic Communications in Probability

On the Non-Convexity of the Time Constant in First-Passage Percolation

Harry Kesten

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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.

Article information

Source
Electron. Commun. Probab., Volume 1 (1996), paper no. 1, 1-6.

Dates
Accepted: 25 January 1996
First available in Project Euclid: 25 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1453756492

Digital Object Identifier
doi:10.1214/ECP.v1-971

Mathematical Reviews number (MathSciNet)
MR1386288

Zentralblatt MATH identifier
0866.60087

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

Keywords
First-passage percolation time constant convexity

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Kesten, Harry. On the Non-Convexity of the Time Constant in First-Passage Percolation. Electron. Commun. Probab. 1 (1996), paper no. 1, 1--6. doi:10.1214/ECP.v1-971. https://projecteuclid.org/euclid.ecp/1453756492


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