Largest Clusters for Supercritical Percolation on Split Trees

Abstract

We consider the model of random trees introduced by Devroye [13], the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation on those trees and obtain a precise weak limit theorem for the sizes of the largest clusters. The approach we develop may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we have also studied the case of complete d-regular trees. 2012 ACM Subject Classification Mathematics of computing → Probabilistic algorithms