DMTCS Proceedings, Discrete Random Walks, DRW'03

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DMTCS Conference vol AC (2003), pp. 95-104


Discrete Random Walks, DRW'03

Cyril Banderier and Christian Krattenthaler (eds.)

DMTCS Conference Volume AC (2003), pp. 95-104

author: Rick Durrett
title: Rigorous Result for the CHKN S Random Graph Model
keywords: random graph, clusterization, Brownian motion, singularity analysis
abstract: We study the phase transition in a random graph in which vertices and edges are added at constant rates. Two recent papers in Physical Review E by Callaway, Hopcroft, Kleinberg, Newman, and Strogatz, and Dorogovstev, Mendes, and Samukhin have computed the critical value of this model, shown that the fraction of vertices in finite clusters is infinitely differentiable at the critical value, and that in the subcritical phase the cluster size distribution has a polynomial decay rate with a continuously varying power. Here we sketch rigorous proofs for the first and third results and a new estimates about connectivity probabilities at the critical value.
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reference: Rick Durrett (2003), Rigorous Result for the CHKN S Random Graph Model, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 95-104
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