# 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.

1999-12-09, Sven Erick Alm, sea@math.uu.se