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

Harry Kesten

Type: Article

Publication Date: 1996-01-01

Citations: 18

DOI: https://doi.org/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.

Locations

Electronic Communications in Probability - View - PDF

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