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Lower and Upper Bounds for the Time Constant of First-Passage Percolation

Published online by Cambridge University Press:  09 October 2002

SVEN ERICK ALM and
ROBERT PARVIAINEN
SVEN ERICK ALM
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: sea@math.uu.se)
ROBERT PARVIAINEN
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: robert@math.uu.se)
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Abstract

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We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates and improved upper confidence limits for the time constants.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 5 , September 2002, pp. 433 - 445
Copyright
2002 Cambridge University Press