Sizes of the largest clusters for supercritical percolation on random recursive trees

Abstract

We consider Bernoulli bond-percolation on a random recursive tree of size n ≫ 1, with supercritical parameter p(n) = 1 - t/ln n + o(1/ln n) for some t > 0 fixed. We show that with high probability, the largest cluster has size close to e -tn whereas the next largest clusters have size of order n/ln n only and are distributed according to some Poisson random measure.