Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas


Journal Article

Let pc(d) be the critical probability for oriented percolation in Zdand let (d) be the time constant for the first passage process based on the exponential distribution. In this paper we show that as d →∞, dpc(d)→ 1 and dμ{d)→γ where y is a constant in [e-1,2-1] which we conjecture to be e-1. In the case of pc(d) we have made some progress toward obtaining an asymptotic expansion in powers of d-1. Our results show The left hand side agrees, up to o(d-3), with a (nonrigorous) series expansion of Blease (1,2). © 1983, Cambridge Philosophical Society. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Cox, JT; Durrett, R

Published Date

  • January 1, 1983

Published In

Volume / Issue

  • 93 / 1

Start / End Page

  • 151 - 162

Electronic International Standard Serial Number (EISSN)

  • 1469-8064

International Standard Serial Number (ISSN)

  • 0305-0041

Digital Object Identifier (DOI)

  • 10.1017/S0305004100060436

Citation Source

  • Scopus