Print Email Facebook Twitter Non-criticality criteria for Abelian sandpile models with sources and sinks Title Non-criticality criteria for Abelian sandpile models with sources and sinks Author Redig, F.H.J. (TU Delft Applied Probability) Ruszel, W.M. (TU Delft Applied Probability) Saada, Ellen (University of Paris) Date 2018 Abstract We prove that the Abelian sandpile model on a random binary and binomial tree, as introduced in Redig, Ruszel, and Saada [J. Stat. Phys. 147, 653-677 (2012)], is not critical for all branching probabilities p < 1; by estimating the tail of the annealed survival time of a random walk on the binary tree with randomly placed traps, we obtain some more information about the exponential tail of the avalanche radius. Next we study the sandpile model on Zd with some additional dissipative sites: we provide examples and sufficient conditions for non-criticality; we also make a connection with the parabolic Anderson model. Finally we initiate the study of the sandpile model with both sources and sinks and give a sufficient condition for non-criticality in the presence of a finite number of sources, using a connection with the homogeneous pinning model. To reference this document use: http://resolver.tudelft.nl/uuid:ea02e1a2-8a28-43d0-ba60-e6fb4910c286 DOI https://doi.org/10.1063/1.5022128 ISSN 0022-2488 Source Journal of Mathematical Physics, 59 (6), 1-16 Part of collection Institutional Repository Document type journal article Rights © 2018 F.H.J. Redig, W.M. Ruszel, Ellen Saada Files PDF 45749400_1.5022128.pdf 353.53 KB Close viewer /islandora/object/uuid:ea02e1a2-8a28-43d0-ba60-e6fb4910c286/datastream/OBJ/view