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The second largest component in the supercritical 2D Hamming graph

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.

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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)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2007-39
Date Deposited: 10 Jul 2008 09:11
URL: http://eprints.lse.ac.uk/6808/

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