相关论文: Convergence of the Abelian sandpile

Emergence is a concept that is easy to exhibit, but very hard to formally handle. This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sandpile is two dimensional, but the support of…

We classify all recurrent configurations of the Abelian sandpile model (ASM) on Ferrers graphs. The classification is in terms of decorations of EW-tableaux, which undecorated are in bijection with the minimal recurrent configurations. We…

We study extreme events in a finite-size 2D Abelian sandpile model, specifically focusing on avalanche area and size. Employing the approach of Block Maxima, the study numerically reveals that the rescaled distributions for the largest…

A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the…

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting…

Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. {\bf 59}, 381 (1987)], and stochastic, such as the Manna model [S.S. Manna, J. Phys. A {\bf 24},…

The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified to allow grains to disappear on each toppling, it is called…

Motivated by the dissipative abelian sandpile model, we analyze the trajectories of a one-dimensional random walk in a landscape of soft traps. These traps, placed at increasing distances from each other, correspond to dissipative sites in…

We show that a fixed set of woven defect lines in a nematic liquid crystal supports a set of non-singular topological states which can be mapped on to recurrent stable configurations in the Abelian sandpile model or chip-firing game. The…

We consider the isotropic two-dimensional abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from…

In this paper we study $\infty$-Laplacian type diffusion equations in weighted graphs obtained as limit as $p\to \infty$ to two types of $p$-Laplacian evolution equations in such graphs. We propose these diffusion equations, that are…

An interesting feature of growth in animals is that different parts of the body grow at approximately the same rate. This property is called proportionate growth. In this paper, we review our recent work on patterns formed by adding $N$…

We consider the Abelian sandpile model on triangular and hexagonal lattices. We compute several height probabilities on the full plane and on half-planes, and discuss some properties of the universality of the model.

Adding sand grains at a single site in Abelian sandpile models produces beautiful but complex patterns. We study the effect of sink sites on such patterns. Sinks change the scaling of the diameter of the pattern with the number $N$ of sand…

In recent work by L. Levine and Y. Peres, it was observed that three models for particle aggregation on the lattice - the divisible sandpile, rotor-router aggregation, and internal diffusion limited aggregation - share a common scaling…

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the…

We study the scaling limits of three different aggregation models on the integer lattice Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform…

We study the probability distribution of residence time, $T$, of the sand grains in the one dimensional abelian sandpile model on a lattice of $L$ sites, for $T<<L^2$ and $T>>L^2$. The distribution function decays as…

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action,…

We introduce a new model of a stochastic sandpile on a graph $G$ containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability $p \in (0,1]$. For $p=1$, this coincides with the standard…