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A remark on the time constant in first-passage percolation

Published online by Cambridge University Press:  01 July 2016

Yves Derriennic
Yves Derriennic*
Affiliation:
Université de Bretagne Occidentale
*
∗Postal address: Faculté des Sciences et Techniques, Département de Mathematiques et Informatique, 6, Avenue Victor le Gorgeu, 29283 Brest Cedex, France.
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Abstract

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It is possible to deduce some information about the time constant μ without using Wierman and Reh's (1978) renewal theorem.

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983, pp. 214 - 215
Copyright
Copyright © Applied Probability Trust 1983 

References

Derriennic, Y. (1980) Quelques applications du théorème ergodique sousadditif. Astérisque 74, 183–201.Google Scholar
Kesten, H. (1980) On the time constant and path length of first passage percolation. Adv. Appl. Prob. 12, 848–863.Google Scholar
Smythe, R. T. and Wierman, J. C. (1978) First-Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Wierman, J. C. (1982) Percolation theory. Ann. Prob. 10, 509–524.Google Scholar
Wierman, J. C. and Reh, W. (1978) On conjectures in first passage percolation theory. Ann. Prob. 6, 388–397.Google Scholar