Abstract
In the Constrained-degree percolation model on a graph (V,E) there are a sequence, (Ue)e∈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 Ue, 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 as on the d-ary regular tree. We also prove that on the square lattice the infinite cluster is unique in the supercritical phase.
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