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A lower bound for the critical probability in a certain percolation process
Abstract
Consider a lattice L in the Cartesian plane consisting of all points (x, y) such that either x or y is an integer. Points with integer coordinates (positive, negative, or zero) are called vertices and the sides of the unit squares (including endpoints) are called links. Each link of L is assigned the designation active with probability p or passive with probability 1 − p, independently of all other links. To avoid trivial cases, we shall always assume 0 < p < 1. The lattice L, with the designations active or passive attached to the links, is called a random maze. A set of links is called connected if the points comprising the links (including endpoints) form a connected point set in the plane.
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Citations
Cited by
Essam, J. W. (1980) · Reports on Progress in Physics · doi:10.1088/0034-4885/43/7/001 · Cited by 1,018
Spatial Contact Models for Ecological and Epidemic Spread
Mollison, D. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01627.x · Cited by 758
Gilbert, E. N. (1961) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0109045 · Cited by 656
Frieze, A., & Karoński, M. (2015) · doi:10.1017/cbo9781316339831 · Cited by 576
Asymptotic independence and limit theorems for positively and negatively dependent random variables
Newman, C. M. (1984) · Institute of Mathematical Statistics Lecture Notes - Monograph Series · doi:10.1214/lnms/1215465639 · Cited by 356
Metadata
- Authors
- Harris, T. E.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1960-01
- Volume
- 56
- Issue
- 1
- Pages
- 13-20
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2097612342
- Cited by
- 589
- References
- 0
- FWCI
- 3.42
- Type
- journal article
- Language
- en
- Open access
- closed
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- Harris, T. E. (1960). A lower bound for the critical probability in a certain percolation process. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100034241
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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