Probability seminar: Scaling limit of dynamical percolation on critical Erdős-Rényi random graphs

15 January 2016, 3.40 PM - 15 January 2016, 4.40 PM

Raphaël Rossignol, Université Grenoble 1

SM3, School of Mathematics

Raphaël Rossignol, Université Grenoble 1

Scaling limit of dynamical percolation on critical Erdős-Rényi random graphs

Consider a critical Erdős-Rényi random graph: n is the number of vertices, each one of the \binom{n}{2} possible edges is kept in the graph independently from the others with probability p(n)=n-1n-4/3, λ being a fixed real number. When n goes to infinity, Addario-Berry, Broutin and Goldschmidt have shown that the collection of connected components, viewed as suitably normalized compact connex metric measure spaces, converge in distribution to a continuous limit made of random real graphs closely linked to the brownian random tree of Aldous. Let us now consider the dynamical percolation on this random graph for finite n. To each pair of vertices is attached a Poisson process of intensity n-1/3, and every time it rings, one resamples the corresponding edge. Under this process, the collection of connected components undergoes coalescence and fragmentation. Motivated by noise sensitivity questions, we shall study the distributional convergence of this process when n goes to infinity, towards a fragmentation-coalescence process on the continuous limit.

Contact information

Organisers: Marton Balazs, Haeran Cho

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