Inequalities for Means of Restricted First-Passage Times in Percolation
Theory
by
Sven Erick Alm and John C. Wierman
Uppsala University and Johns Hopkins University
U.U.D.M. Report 1997:27, ISSN 1101-3591
In Combinatorics, Probability and Computing (1999) 8, 307-315
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.