## 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.

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## Published In

Mathematical Proceedings of the Cambridge Philosophical Society

## DOI

## EISSN

1469-8064

## ISSN

0305-0041

## Publication Date

January 1, 1983

## Volume

93

## Issue

1

## Start / End Page

151 / 162

## Related Subject Headings

- 0101 Pure Mathematics

### Citation

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MLA

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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/S0305004100060436Cox, 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

## EISSN

1469-8064

## ISSN

0305-0041

## Publication Date

January 1, 1983

## Volume

93

## Issue

1

## Start / End Page

151 / 162

## Related Subject Headings

- 0101 Pure Mathematics