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Rigorous Self-organised Criticality in the Modified Bak-Sneppen Model

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Abstract

We prove that a modified version of the Bak-Sneppen model obeys power law behaviour for avalanche duration and size. We do this through a coupling with a suitable branching process which is known to have power law behaviour at criticality.

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References

  1. Bak, P.: How Nature Works. Springer, Berlin (1996)

    MATH  Google Scholar 

  2. Bak, P., Sneppen, K.: Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 74, 4083 (1993)

    Article  ADS  Google Scholar 

  3. Ben-Ari, I., Matzavinos, A., Roitershtein, A.: On a species survival model. Electron. Commun. Probab. 16, 226–233 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Guiol, H., Machado, F.P., Schinazi, R.B.: A stochastic model of evolution. Markov Process. Relat. Fields 17, 253–258 (2011)

    MathSciNet  MATH  Google Scholar 

  5. Harris, T.E.: The Theory of Branching Processes. Springer, Berlin (1963)

    Book  MATH  Google Scholar 

  6. Jensen, H.J.: In: Self-organized Criticality. Cambridge Lecture Notes in Physics (1998)

    Chapter  Google Scholar 

  7. Meester, R., Znamenski, D.: Limit behavior of the Bak-Sneppen evolution model. Ann. Probab. 31, 1986–2002 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Meester, R., Znamenski, D.: Critical thresholds and the limit distribution in the Bak-Sneppen evolution model. Commun. Math. Phys. 246, 63–86 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, VU Universiteit Amsterdam, Amsterdam, The Netherlands

    Ronald Meester

  2. Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi, 110016, India

    Anish Sarkar

Authors
  1. Ronald Meester
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  2. Anish Sarkar
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Correspondence to Ronald Meester.

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Meester, R., Sarkar, A. Rigorous Self-organised Criticality in the Modified Bak-Sneppen Model. J Stat Phys 149, 964–968 (2012). https://doi.org/10.1007/s10955-012-0627-2

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  • DOI: https://doi.org/10.1007/s10955-012-0627-2

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