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Breakage and restoration in recursive trees

Part of: Graph theory Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Guillermo Tomás Tetzlaff
Guillermo Tomás Tetzlaff*
Affiliation:
Universidad de Buenos Aires and Universidad Nacional de La Plata
*
∗ Postal address: Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Pabelló I, Ciudad Universitaria, (1428) Buenos Aires, Argentina. Email address: tetzlaff@dc.uba.ar
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Abstract

Uniform sequential tree-building aggregation of n particles is analyzed together with the effect of the avalanche that takes place when a subtree rooted at a uniformly chosen vertex is removed. For large n, the expected subtree size is found to be ≃ logn both for the tree of size n and the tree that remains after an avalanche. Repeated breakage-restoration cycles are seen to give independent avalanches which attain size k(1 ≤ k ≤ n-1) with probability (k(k+1))-1 and restored trees that are recursive.

Keywords

Aggregationrecursive treeavalancheself-organized criticality

MSC classification

Primary: 60C05: Combinatorial probability 05C80: Random graphs
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 383 - 390
Copyright
Copyright © Applied Probability Trust 2002 

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