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Maximal avalanches in the Bak-Sneppen model

Published online by Cambridge University Press:  14 July 2016

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: [email protected]
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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.

Type
Research Article
Copyright
© Applied Probability Trust 2006 

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