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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 36 open journal systems 


Continuity of the percolation threshold in randomly grown graphs.

Tatyana S. Turova, Lund University, Sweden


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.


Full text: PDF

Pages: 1036-1047

Published on: August 9, 2007


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Electronic Journal of Probability. ISSN: 1083-6489