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Phase transition and critical behavior in a model of organized criticality
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  • Published: 14 October 2003

Phase transition and critical behavior in a model of organized criticality

  • M. Biskup1,
  • Ph. Blanchard2,
  • L. Chayes1,
  • D. Gandolfo3 &
  • …
  • T. Krüger2 

Probability Theory and Related Fields volume 128, pages 1–41 (2004)Cite this article

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Abstract.

We study a model of ‘‘organized’’ criticality, where a single avalanche propagates through an a priori static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel probability measure ρ on [0,1]. The avalanche dynamics is driven by a standard toppling rule, however, we simplify the geometry by placing the problem on a directed, rooted tree. As our main result, we characterize which ρ are critical in the sense that they do not admit an infinite avalanche but exhibit a power-law decay of avalanche sizes. Our analysis reveals close connections to directed site-percolation, both in the characterization of criticality and in the values of the critical exponents.

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Author information

Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, California, USA

    M. Biskup & L. Chayes

  2. Department of Theoretical Physics, University of Bielefeld, Bielefeld, Germany

    Ph. Blanchard & T. Krüger

  3. Phymath, Department of Mathematics, University of Toulon, Toulon, France and CPT/CNRS, Luminy, Marseille, France

    D. Gandolfo

Authors
  1. M. Biskup
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  2. Ph. Blanchard
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  3. L. Chayes
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  4. D. Gandolfo
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  5. T. Krüger
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Additional information

Mathematics Subject Classification (2000): 60K35, 82C20, 82C44

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Biskup, M., Blanchard, P., Chayes, L. et al. Phase transition and critical behavior in a model of organized criticality. Probab. Theory Relat. Fields 128, 1–41 (2004). https://doi.org/10.1007/s00440-003-0269-z

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  • Received: 03 June 2002

  • Revised: 25 February 2003

  • Published: 14 October 2003

  • Issue Date: January 2004

  • DOI: https://doi.org/10.1007/s00440-003-0269-z

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Keywords

  • Phase Transition
  • Probability Measure
  • Critical Exponent
  • Rooted Tree
  • Close Connection
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