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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References
R. Arratia (1981) ArticleTitleLimit processes for rescalings of coalescing and annihilating random walks on Zd Annals Probab. 9 909–936
P. Bak K. Sneppen (1993) ArticleTitlePunctuated equilibrium and criticality in a simple model of evolution Phys. Rev. Lett. 71 4083–4086 Occurrence Handle10.1103/PhysRevLett.71.4083 Occurrence Handle10055149
C. Bandt (1999) ArticleTitleThe geometry of a parameter space of interacting particle systems. J. Stat. Phys. 96 883–906 Occurrence Handle10.1023/A:1004614827017
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)
J. Boer Particlede B. Derrida H. Flygberg A.D. Jackson T. Wettig (1994) ArticleTitleSimple model of self-organized biological evolution Phys. Rev. Lett. 73 906–909 Occurrence Handle10.1103/PhysRevLett.73.906 Occurrence Handle10057569
P. Grassberger (1995) ArticleTitleThe Bak–Sneppen model for punctuated evolution Phys. Lett. A 200 277–282 Occurrence Handle10.1016/0375-9601(95)00179-7
T.E. Harris (1974) ArticleTitleContact interactions on a lattice Ann. Probab. 2 969–988
D.A. Head G. J. Rogers (1998) ArticleTitleThe anisotropic Bak–Sneppen model J. Phys. A 31 3977–3984
T.M. Liggett, Interacting Particle Systems (Springer 1985)
T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, (Springer, 1999)
S. Maslov P. los Rios Particlede M. Marsili Y. Zhang (1998) ArticleTitleCritical exponents of the anisotropic Bak–Sneppen model Phys Rev. 58 7141–7145 Occurrence Handle10.1103/PhysRevB.58.7141
R. Meester D. Znamenski (2002) ArticleTitleNon-triviality of a discrete Bak–Sneppen evolution model J. Stat. Phys. 109 987–1004 Occurrence Handle10.1023/A:1020468325294
R. Meester D. Znamenski (2003) ArticleTitleLimit behavior of the Bak–Sneppen evolution model Ann. Probab. 31 1986–2002 Occurrence Handle10.1214/aop/1068646375
R.B. Schinazi, Classical and Spatial Stochastic Processes, (Birkhäuser, 1999)
A. Sudbury P. Lloyd (1997) ArticleTitleQuantum operators in classical probability: IV. Quasi-duality and thinnings of interacting particle systems Ann. Probab. 25 96–114 Occurrence Handle10.1214/aop/1024404280
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Bandt, C. The Discrete Evolution Model of Bak and Sneppen is Conjugate to the Classical Contact Process. J Stat Phys 120, 685–693 (2005). https://doi.org/10.1007/s10955-005-5965-x
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DOI: https://doi.org/10.1007/s10955-005-5965-x