TY - JOUR

T1 - Oriented Percolation in Dimensions D ≥ 4

T2 - Bounds and Asymptotic Formulas

AU - Cox, J Theodore

AU - Durrett, Richard

PY - 1983

Y1 - 1983

N2 - 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).

AB - 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).

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U2 - 10.1017/S0305004100060436

DO - 10.1017/S0305004100060436

M3 - Article

AN - SCOPUS:84976077801

VL - 93

SP - 151

EP - 162

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -