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Journal of Statistical Physics

, Volume 74, Issue 3–4, pp 607–630 | Cite as

Fluctuations in mean-field self-organized criticality

  • B. Gaveau
  • L. S. Schulman
Article

Abstract

We present two models that exhibit self-organized criticality at the mean-field level. These can be variously interpreted in epidemiological or chemical reaction terms. By studying the master equation for these models we find, however, that only in one of them does the self-organized critical behavior survive in the face of fluctuations. For this model we show the spectrum of the evolution operator to have spectral collapse, i.e., instead of a gap, as would occur in noncritical behavior, there are eigenvalues that approach zero as an inverse power of system size.

Key Words

Self-organized criticality directed percolation epidemic models chemical reactions transfer matrix spectral collapse 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • B. Gaveau
    • 1
  • L. S. Schulman
    • 2
  1. 1.MathématiquesUniversité P. M. CurieParis Cedex 05France
  2. 2.Physics DepartmentClarkson UniversityPotsdam

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