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

J Theodore Cox, Richard Durrett

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

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).

Original languageEnglish (US)
Pages (from-to)151-162
Number of pages12
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume93
Issue number1
DOIs
StatePublished - 1983

ASJC Scopus subject areas

  • Mathematics(all)

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