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Maximal avalanches in the Bak-Sneppen model. (English) Zbl 1127.60089

The paper is devoted to study the durations of the avalanches in the maximal avalanche decomposition of the Bak-Sneppen evolution model. The authors show that all the avalanches in this maximal decomposition have infinite expectation. Also they show that only barely (the appropriate threshold a tiny amount smaller) then, the avalanches would have finite expectation.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82C22 Interacting particle systems in time-dependent statistical mechanics
60J99 Markov processes
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References:

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