Growth Rates and Explosions in Sandpiles (2009)
Fey, Anne, Levine, Lionel, Peres, Yuval
We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z^d. Any site with at least 2d particles then topples by sending one...
Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model (2008)
Fey, Anne, Liu, Haiyan, Meester, Ronald
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 = 1, \mu is not stabilizable; for 1/2
Fey, Anne, Van Der Hofstad, Remco, Klok, Marten
We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the...
Stabilizability and percolation in the infinite volume sandpile model (2007)
Fey, Anne, Meester, Ronald, Redig, Frank
We study the sandpile model in infinite volume on $\Zd$. In particular we are interested in relations between the density $\rho$ of a stationary measure $\mu$ on initial configurations, and the...
Limiting shapes for deterministic centrally seeded growth models (2007)
We study the rotor router model and two deterministic sandpile models. For the rotor router model in $\mathbb{Z}^d$, Levine and Peres proved that the limiting shape of the growth cluster is a sphere....
A probabilistic approach to Zhang's sandpile model (2007)
Fey, Anne, Meester, Ronald, Quant, Corrie, Redig, Frank
The current literature on sandpile models mainly deals with the abelian sandpile model (ASM) and its variants. We treat a less known - but equally interesting - model, namely Zhang's sandpile. This...