TY - JOUR
T1 - Mean-field avalanche size exponent for sandpiles on Galton–Watson trees
AU - Jarai, Antal A.
AU - Ruszel, Wioletta M.
AU - Saada, Ellen
PY - 2019
Y1 - 2019
N2 - We show that in Abelian sandpiles on infinite Galton–Watson trees, the probability that the total avalanche has more than t topplings decays as t- 1 / 2. We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (Probab Theory Relat Fields 125:259–265, 2003), that was previously used by Lyons et al. (Electron J Probab 13(58):1702–1725, 2008) to study uniform spanning forests on Zd, d≥ 3 , and other transient graphs.
AB - We show that in Abelian sandpiles on infinite Galton–Watson trees, the probability that the total avalanche has more than t topplings decays as t- 1 / 2. We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (Probab Theory Relat Fields 125:259–265, 2003), that was previously used by Lyons et al. (Electron J Probab 13(58):1702–1725, 2008) to study uniform spanning forests on Zd, d≥ 3 , and other transient graphs.
KW - Abelian sandpile
KW - Conductance martingale
KW - Uniform spanning tree
KW - Wired spanning forest
UR - http://www.scopus.com/inward/record.url?scp=85074829430&partnerID=8YFLogxK
U2 - 10.1007/s00440-019-00951-z
DO - 10.1007/s00440-019-00951-z
M3 - Article
AN - SCOPUS:85074829430
SN - 0178-8051
VL - 177 (2020)
SP - 369
EP - 396
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 1-2
ER -