The Discrete Evolution Model of Bak and Sneppen is Conjugate to the Classical Contact Process
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Two fundamental models of critical phenomena are connected. We show that the discrete Bak–Sneppen evolution model is conjugate to the classical contact process. This holds in discrete and continuous time, on all graphs and for random as well as for deterministic choice of neighbors. Thus the extensive theory for the contact process applies to the discrete Bak–Sneppen model, too.
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Contact process cellular automata thinning self-organized criticality evolution modelPreview
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References
- 1.Arratia, R. 1981Limit processes for rescalings of coalescing and annihilating random walks on ZdAnnals Probab.9909936Google Scholar
- 2.Bak, P., Sneppen, K. 1993Punctuated equilibrium and criticality in a simple model of evolutionPhys. Rev. Lett.7140834086CrossRefPubMedGoogle Scholar
- 3.Bandt, C. 1999The geometry of a parameter space of interacting particle systems.J. Stat. Phys.96883906CrossRefGoogle Scholar
- 4.J. Barbay, C. Kenyon, On the discrete Bak–Sneppen model of self-organized criticality, In Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms, Washington DC (2001)Google Scholar
- 5.Boer, J., Derrida, B., Flygberg, H., Jackson, A.D., Wettig, T. 1994Simple model of self-organized biological evolutionPhys. Rev. Lett.73906909CrossRefPubMedGoogle Scholar
- 6.Grassberger, P. 1995The Bak–Sneppen model for punctuated evolutionPhys. Lett. A200277282CrossRefGoogle Scholar
- 7.Harris, T.E. 1974Contact interactions on a latticeAnn. Probab.2969988Google Scholar
- 8.Head, D.A., Rogers, G. J. 1998The anisotropic Bak–Sneppen modelJ. Phys. A3139773984Google Scholar
- 9.T.M. Liggett, Interacting Particle Systems (Springer 1985)Google Scholar
- 10.T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, (Springer, 1999)Google Scholar
- 11.Maslov, S., los Rios, P., Marsili, M., Zhang, Y. 1998Critical exponents of the anisotropic Bak–Sneppen modelPhys Rev.5871417145CrossRefGoogle Scholar
- 12.Meester, R., Znamenski, D. 2002Non-triviality of a discrete Bak–Sneppen evolution modelJ. Stat. Phys.1099871004CrossRefGoogle Scholar
- 13.Meester, R., Znamenski, D. 2003Limit behavior of the Bak–Sneppen evolution modelAnn. Probab.3119862002CrossRefGoogle Scholar
- 14.R.B. Schinazi, Classical and Spatial Stochastic Processes, (Birkhäuser, 1999)Google Scholar
- 15.Sudbury, A., Lloyd, P. 1997Quantum operators in classical probability: IV. Quasi-duality and thinnings of interacting particle systemsAnn. Probab.2596114CrossRefGoogle Scholar
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