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

   
@article{ECP971,
	author = {Harry Kesten},
	title = {On the Non-Convexity of the Time Constant in First-Passage Percolation},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {1},
	year = {1996},
	keywords = {First-passage percolation, time constant, convexity.},
	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.},
	pages = {no. 1, 1-6},
	issn = {1083-589X},
	doi = {10.1214/ECP.v1-971},    
        url = {http://ecp.ejpecp.org/article/view/971}}