TY - JOUR
T1 - Non-criticality criteria for Abelian sandpile models with sources and sinks
AU - Redig, Frank
AU - Ruszel, Wioletta M.
AU - Saada, Ellen
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85049555624&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:ea02e1a2-8a28-43d0-ba60-e6fb4910c286
U2 - 10.1063/1.5022128
DO - 10.1063/1.5022128
M3 - Article
AN - SCOPUS:85049555624
SN - 0022-2488
VL - 59
SP - 1
EP - 16
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 6
M1 - 063302
ER -