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
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
APA
Chicago
ICMJE
MLA
NLM
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
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