4 papers
Derivative formula for capacities
Amine Asselah, Bruno Schapira, Perla Sousi
We obtain a derivative formula for various notions of capacity. Namely we identify the second order term in the asymptotic expansion of the capacity of a union of two sets, as thei…
Covering a graph with independent walks
Jonathan Hermon, Perla Sousi
Let be an irreducible and reversible transition matrix on a finite state space with invariant distribution . We let chains start by choosing independent locations d…
Capacity in high dimensional percolation
Amine Asselah, Bruno Schapira, Perla Sousi
We introduce a notion of capacity for high dimensional critical percolation by showing that for any finite set , the suitably rescaled probability that the cluster of inters…
Cutoff for random walk on random graphs with a community structure
Jonathan Hermon, AnÄela Å arkoviÄ, Perla Sousi
We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $\…