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

Authors:
Sven Erick Alm;John C. Wierman
Affiliations:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: sea@math.uu.se);Mathematical Sciences Department, The Johns Hopkins University, Baltimore, MD 21218-2682, USA (e-mail: wierman@jhu.edu)
Venue:
Combinatorics, Probability and Computing
Year:
1999

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Abstract

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.