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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.

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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[1] Bak, P. (1996). How Nature Works . Springer, New York. · Zbl 0894.00007
[2] Bak, P. and Sneppen, K. (1993). Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 74 4083–4086.
[3] de Boer, J., Derrida, B., Flyvbjerg, H., Jackson, A. D. and Wettig, T. (1994). Simple model of self-organized biological evolution. Phys. Rev. Lett. 73 906–909.
[4] Jensen, H. J. (1998). Self-Organized Criticality . Cambridge Univ. Press. · Zbl 0945.70001
[5] Maslov, S. (2001). Infinite hierarchy of exact equations in the Bak–Sneppen model.
[6] Meester, R. and Znamenski, D. (2002). Non-triviality of the discrete Bak–Sneppen evolution model. J. Statist. Phys. 109 987–1004. · Zbl 1015.92028
[7] Yamano, T. (2001). Regulation effects on market with Bak–Sneppen model in high dimensions. Internat. J. Modern Phys. C . 12 1329–1333.
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