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2007 Continuity of the percolation threshold in randomly grown graphs.
Tatyana Turova
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Electron. J. Probab. 12: 1036-1047 (2007). DOI: 10.1214/EJP.v12-436

Abstract

We consider various models of randomly grown graphs. In these models the vertices and the edges accumulate within time according to certain rules. We study a phase transition in these models along a parameter which refers to the mean life-time of an edge. Although deleting old edges in the uniformly grown graph changes abruptly the properties of the model, we show that some of the macro-characteristics of the graph vary continuously. In particular, our results yield a lower bound for the size of the largest connected component of the uniformly grown graph.

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Tatyana Turova. "Continuity of the percolation threshold in randomly grown graphs.." Electron. J. Probab. 12 1036 - 1047, 2007. https://doi.org/10.1214/EJP.v12-436

Information

Accepted: 9 August 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.05095
MathSciNet: MR2336597
Digital Object Identifier: 10.1214/EJP.v12-436

Subjects:
Primary: 05C80
Secondary: 60J80 , 82C20

Keywords: branching processes , Dynamic random graphs , phase transition

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Vol.12 • 2007
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