5 citations · 6 across the 3 of their papers we have counts for
3 papers
math.CO2010★ 5 cited
Limiting shapes for a non-abelian sandpile growth model and related cellular automata
Anne Fey, Haiyan Liu
We present limiting shape results for a non-abelian variant of the abelian sandpile growth model (ASGM), some of which have no parallel in the ASGM. One of our limiting shapes is a…
math.PR2009★ 1 cited
Existence and uniqueness of the stationary measure in the continuous Abelian sandpile
Wouter Kager, Haiyan Liu, Ronald Meester
Let Λbe a finite subset of Z^d. We study the following sandpile model on Λ. The height at any given vertex x of Λis a positive real number, and additions are uniformly distributed…
math-ph2008
Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model
Anne Fey, Haiyan Liu, Ronald Meester
We show that Zhang's sandpile model (N,[a,b]) on N sites and with uniform additions on [a,b] has a unique stationary measure for all 0 <= a < b <= 1. This generalizes earlier resul…