Organized versus self-organized criticality in the abelian sandpile model

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103533We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense the thermodynamic limit of the uniform measures on the recurrent configurations of the abelian sandpile model (ASM) is a maximal element of the set of stabilizable measures. In that sense the self-organized critical behavior of the ASM can be understood in terms of an ordinary transition between stabilizable and non-stabilizable17 pages, appeared in Markov Processes and Related Fields 2005Mathematical PhysicsProbability60K35, 82C22Organized versus self-organized criticality in the abelian sandpile modeltext