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Limit behavior of the Bak-Sneppen evolution model. (English) Zbl 1044.60095
A main problem for the Bak-Sneppen evolution model on the circle is computing the limit distribution of the fitness at a fixed observation vertex in the stationary regime as the size of the system tends to infinity. It is proven that the mean of the fitness in the stationary regime is bounded away from 1, uniformly in the size of the system. The Bak-Sneppen dynamics can be defined on any finite connected graph. Using a “self-similar” graphical representation of the avalanches a generalization of the phase-transition result in the context of an increasing sequence of such graphs is given.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
92B15 General biostatistics
82B26 Phase transitions (general) in equilibrium statistical mechanics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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References:
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