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A Note on a Problem by Welsh in First-Passage Percolation

Published online by Cambridge University Press:  01 March 1998

SVEN ERICK ALM
SVEN ERICK ALM
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden
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Abstract

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Consider first-passage percolation on the square lattice. Welsh, who together with Hammersley introduced the subject in 1963, has formulated a problem about mean first-passage times, which, although seemingly simple, has not been proved in any non-trivial case. In this paper we give a general proof of Welsh's problem.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 1 , March 1998 , pp. 11 - 15
Copyright
1998 Cambridge University Press