Phase transition and critical behavior in a model of organized criticality

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dc.creatorBiskup, Marek
dc.creatorBlanchard, Philippe
dc.creatorChayes, Lincoln
dc.creatorGandolfo, Daniel
dc.creatorKrueger, Tyll
dc.date2002-06-21
dc.date2003-09-30
dc.date.accessioned2026-07-07T04:49:18Z
dc.date.available2026-07-07T04:49:18Z
dc.descriptionWe study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{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.
dc.description37 pages, version to appear in Prob. Theory Rel. Fields
dc.identifierhttps://arxiv.org/abs/math/0206232
dc.identifierhttp://arxiv.org/abs/math/0206232
dc.identifierProbab. Theory Rel. Fields 128 (2004), no. 1, 1-41.
dc.identifierdoi:10.1007/s00440-003-0269-z
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64368
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject82C27; 60K35
dc.titlePhase transition and critical behavior in a model of organized criticality
dc.typetext

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