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Largest Clusters for Supercritical Percolation on Split Trees

Authors Gabriel Berzunza , Cecilia Holmgren

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Author Details

Gabriel Berzunza
  • Department of Mathematics, Uppsala University, Sweden
Cecilia Holmgren
  • Department of Mathematics, Uppsala University, Sweden

Funding

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.

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Gabriel Berzunza and Cecilia Holmgren. Largest Clusters for Supercritical Percolation on Split Trees. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.AofA.2020.6

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • Split trees
  • random trees
  • supercritical bond-percolation
  • cluster size
  • Poisson measures

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