Groningen Stochastic Seminar - Prof. B.N.B. de Lima - Federal University of Minas Gerais

Title: The Constrained-degree percolation model

Abstract:

In the Constrained-degree percolation model on a graph (V,E) there are a sequence,  (U_e)_{e є E}, of i.i.d. random variables with distribution U[0,1] and a positive integer k. Each bond e tries to open at time U_e, it succeeds if both its end-vertices would have degrees at most k-1. We prove a phase transition theorem for this model on the square lattice L² , as well on the d-ary regular tree. We also prove that on the square lattice the infinite cluster is unique in the supercritical phase. Joint work with R. Sanchis, D. dos Santos, V. Sidoravicius and R. Teodoro.