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On a Form of Coordinate Percolation

Published online by Cambridge University Press:  01 November 2008

ELIZABETH R. MOSEMAN  and
PETER WINKLER
ELIZABETH R. MOSEMAN
Affiliation:
Department of Mathematical Sciences, USMA, West Point NY 10996, USA (e-mail: lizz.moseman@usma.edu)
PETER WINKLER
Affiliation:
Department of Mathematics, Dartmouth College, Hanover NH 03755-3551, USA (e-mail: peter.winkler@dartmouth.edu)
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Abstract

Let ai,bi, i = 0, 1, 2, . . . be drawn uniformly and independently from the unit interval, and let t be a fixed real number. Let a site (i, j) ∈ be open if ai + bj ≤ t, and closed otherwise. We obtain a simple, exact expression for the probability Θ(t) that there is an infinite path (oriented or not) of open sites, containing the origin. Θ(t) is continuous and has continuous first derivative except at the critical point (t=1), near which it has critical exponent (3 − )/2.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 6 , November 2008 , pp. 837 - 845
Copyright
Copyright © Cambridge University Press 2008

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