Continuity of the percolation threshold in randomly grown graphs

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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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Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics
Original languageEnglish
Pages (from-to)1036-1047
JournalElectronic Journal of Probability
Volume12
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes