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Raphaël Rossignol (colloque Swansea - Grenoble)

Scaling limits of dynamical percolation on critical Erdös-Rényi random graphs
Mardi, 12 Septembre, 2017 - 14:00
Résumé : 

An Erdös-Rényi random graph with parameters p and n is a graph on n vertices where each possible edge is present with probability p, independently from the others. When n is large, there is a particular scaling of p where one assists to the appearance of a giant connected component. Inside this "critical" window, focusing on the largest components, Addario-Berry, Broutin and Goldschmidt have shown in 2012 that one may renormalize the components in order to obtain convergence in distribution, when the number of vertices n goes to infinity, to a collection of random graphs that we shall call the CER (for Continuous Erdös-Rényi random graph). The aim of this talk is to explain what is the limit, as n goes to infinity, of a special resampling procedure of the Erdös-Rényi random graph (dynamical percolation).

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