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

Harry Kesten (Cornell University)

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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Pages: 1-6

Publication Date: January 25, 1996

DOI: 10.1214/ECP.v1-971

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