Scholars@Duke publication: Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas

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

Publication , Journal Article

Cox, JT; Durrett, R

Published in: Mathematical Proceedings of the Cambridge Philosophical Society

January 1, 1983

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.

Duke Scholars

Author Richard Timothy Durrett Mathematics

Published In

Mathematical Proceedings of the Cambridge Philosophical Society

DOI

10.1017/S0305004100060436

EISSN

1469-8064

ISSN

0305-0041

Publication Date

January 1, 1983

Volume

Issue

Start / End Page

151 / 162

Related Subject Headings

4904 Pure mathematics
0101 Pure Mathematics

Citation

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Cox, J. T., & Durrett, R. (1983). Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas. Mathematical Proceedings of the Cambridge Philosophical Society, 93(1), 151–162. https://doi.org/10.1017/S0305004100060436

Cox, J. T., and R. Durrett. “Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas.” Mathematical Proceedings of the Cambridge Philosophical Society 93, no. 1 (January 1, 1983): 151–62. https://doi.org/10.1017/S0305004100060436.

Cox JT, Durrett R. Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas. Mathematical Proceedings of the Cambridge Philosophical Society. 1983 Jan 1;93(1):151–62.

Cox, J. T., and R. Durrett. “Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 93, no. 1, Jan. 1983, pp. 151–62. Scopus, doi:10.1017/S0305004100060436.

Cox JT, Durrett R. Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas. Mathematical Proceedings of the Cambridge Philosophical Society. 1983 Jan 1;93(1):151–162.

Published In

Mathematical Proceedings of the Cambridge Philosophical Society

DOI

10.1017/S0305004100060436

EISSN

1469-8064

ISSN

0305-0041

Publication Date

January 1, 1983

Volume

Issue

Start / End Page

151 / 162

Related Subject Headings

4904 Pure mathematics
0101 Pure Mathematics