Sizes of the largest clusters for supercritical percolation on random recursive trees. Issue 1 (17th July 2012) - Bertoin, Jean
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⁡nonly and are distributed according to some Poisson random measure. Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 29–44, 2014