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Maximal avalanches in the Bak-Sneppen model

Part of: Special processes Equilibrium statistical mechanics Markov processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  14 July 2016

Alexis Gillett ,
Ronald Meester  and
Peter van der Wal
Alexis Gillett*
Affiliation:
Vrije Universiteit Amsterdam
Ronald Meester*
Affiliation:
Vrije Universiteit Amsterdam
Peter van der Wal*
Affiliation:
EURANDOM
*
∗Postal address: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands.
∗Postal address: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands.
∗∗∗∗Postal address: EURANDOM, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: vanderwal@eurandom.tue.nl
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Abstract

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We study the durations of the avalanches in the maximal avalanche decomposition of the Bak-Sneppen evolution model. We show that all the avalanches in this maximal decomposition have infinite expectation, but only ‘barely’, in the sense that if we made the appropriate threshold a tiny amount smaller (in a certain sense), then the avalanches would have finite expectation. The first of these results is somewhat surprising, since simulations suggest finite expectations.

Keywords

Bak-Sneppen evolution modelavalancheself-organised criticality

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82C22: Interacting particle systems 60J99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 840 - 851
Copyright
© Applied Probability Trust 2006 

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