conjecture</A> 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 $ZZ^d$ for $d$ large.">
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 Electronic Communications in Probability > Vol. 1 (1996) > Paper 1 open journal systems 


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 $ZZ^d$ for $d$ large.


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Pages: 1-6

Published on: January 25, 1996
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Electronic Communications in Probability. ISSN: 1083-589X