Phase transition and critical behavior in a model of organized criticality

Biskup M, Blanchard P, Chayes L, Gandolfo D, Krüger T (2004)
PROBABILITY THEORY AND RELATED FIELDS 128(1): 1-41.

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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 rho 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 rho 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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Biskup M, Blanchard P, Chayes L, Gandolfo D, Krüger T. Phase transition and critical behavior in a model of organized criticality. PROBABILITY THEORY AND RELATED FIELDS. 2004;128(1):1-41.
Biskup, M., Blanchard, P., Chayes, L., Gandolfo, D., & Krüger, T. (2004). Phase transition and critical behavior in a model of organized criticality. PROBABILITY THEORY AND RELATED FIELDS, 128(1), 1-41.
Biskup, M., Blanchard, P., Chayes, L., Gandolfo, D., and Krüger, T. (2004). Phase transition and critical behavior in a model of organized criticality. PROBABILITY THEORY AND RELATED FIELDS 128, 1-41.
Biskup, M., et al., 2004. Phase transition and critical behavior in a model of organized criticality. PROBABILITY THEORY AND RELATED FIELDS, 128(1), p 1-41.
M. Biskup, et al., “Phase transition and critical behavior in a model of organized criticality”, PROBABILITY THEORY AND RELATED FIELDS, vol. 128, 2004, pp. 1-41.
Biskup, M., Blanchard, P., Chayes, L., Gandolfo, D., Krüger, T.: Phase transition and critical behavior in a model of organized criticality. PROBABILITY THEORY AND RELATED FIELDS. 128, 1-41 (2004).
Biskup, M, Blanchard, Philippe, Chayes, L, Gandolfo, D, and Krüger, Tyll. “Phase transition and critical behavior in a model of organized criticality”. PROBABILITY THEORY AND RELATED FIELDS 128.1 (2004): 1-41.
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