Largest Clusters for Supercritical Percolation on Split Trees
- Mathematics of computing → Probabilistic algorithms
Abstract. We consider the model of random trees introduced by Devroye [Devroye, 1999], 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.
This work is supported by the Knut and Alice Wallenberg Foundation, the Swedish Research Council and The Swedish Foundations' starting grant from Ragnar Söderbergs Foundation.