Luczak, Malwina and Spencer, J (2007) The second largest component in the supercritical 2D Hamming graph. LSE-CDAM-2007-39. London school of economics and political science, London, UK.
Full text not available from this repository.Abstract
The 2-dimensional Hamming graph H(2,n) consists of the n2 vertices (i,j), 1≤ i,j≤ n, two vertices being adjacent when they share a common coordinate. We examine random subgraphs of H(2,n) in percolation with edge probability p, so that the average degree 2(n-1)p=1+ε. Previous work [5] had shown that in the barely supercritical region n-2/3 ln1/3n << ε << 1 the largest component has size ~ 2εn. Here we show that the second largest component has size close to ε-2, so that the dominant component has emerged.
| Item Type: | Monograph (Report) |
|---|---|
| Official URL: | http://www.cdam.lse.ac.uk/Reports/ |
| Additional Information: | © 2007 London school of economics and political science |
| Library of Congress subject classification: | H Social Sciences > H Social Sciences (General) |
| Sets: | Departments > Mathematics Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM) |
| Identification Number: | LSE-CDAM-2007-39 |
| Date Deposited: | 10 Jul 2008 09:11 |
| URL: | http://eprints.lse.ac.uk/6808/ |
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