2002/06/30 by Marek Biskup, Philippe Blanchard, Ph. Blanchard +5
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35 #msc:82C27
paper · pdf · doi:10.1007/s00440-003-0269-z
published as Probab. Theory Rel. Fields 128 (2004), no. 1, 1-41. · 37 pages, version to appear in Prob. Theory Rel. Fields
arxiv created 2003/09/30 · openalex publication_date 2003/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.