The asymptotic distribution of cluster sizes for supercritical percolation on random split trees. Issue 4 (20th September 2021)

• Record Type: Journal Article
• Authors: Berzunza, Gabriel; Holmgren, Cecilia
• Is Part Of: Random structures & algorithms. Volume 60:Issue 4(2022)
• Page Start: 631
• Page End: 652
• Publication Date: 2021-09-20
• Subjects: cluster size -- Poisson processes -- random trees -- split trees -- supercritical bond‐percolation; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.21046
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: We consider the model of random trees introduced by Devroye, 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. We also show that the approach developed in this work may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we also study the case of d ‐regular trees.