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


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.


Download Citation

Tatyana Turova. "Continuity of the percolation threshold in randomly grown graphs.." Electron. J. Probab. 12 1036 - 1047, 2007.


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

Primary: 05C80
Secondary: 60J80 , 82C20

Keywords: branching processes , Dynamic random graphs , phase transition

Vol.12 • 2007
Back to Top