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Cutting Edges at Random in Large Recursive Trees

  • Erich Baur
  • Jean BertoinEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 100)

Abstract

We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or disconnect certain distinguished vertices when the size of the tree tends to infinity. New probabilistic explanations are given in terms of the so-called cut-tree and the tree of component sizes, which both encode different aspects of the destruction process. Finally, we establish the connection to Bernoulli bond percolation on large RRT’s and present recent results on the cluster sizes in the supercritical regime.

Keywords

Random recursive tree Destruction of graphs Isolation of nodes Disconnection Supercritical percolation Cluster sizes Fluctuations 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.ENS LyonLyonFrance
  2. 2.Universität ZürichZürichSwitzerland

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