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Inequalities for Means of Restricted First-Passage Times in Percolation Theory

Published online by Cambridge University Press:  01 July 1999

SVEN ERICK ALM  and
JOHN C. WIERMAN
SVEN ERICK ALM
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: sea@math.uu.se)
JOHN C. WIERMAN
Affiliation:
Mathematical Sciences Department, The Johns Hopkins University, Baltimore, MD 21218-2682, USA (e-mail: wierman@jhu.edu)
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Abstract

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A simple geometric argument establishes an inequality between the sums of two pairs of first-passage times. This result is used to prove monotonicity, convexity and concavity results for first-passage times with cylinder and half-space restrictions.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 4 , July 1999 , pp. 307 - 315
Copyright
1999 Cambridge University Press