Related papers: Inequalities for critical exponents in $d$-dimensi…
We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang and Wiesenfeld model {[}P.Bak, C. Tang, and K. Wiesenfeld, Phys. Rev.…
We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that…
We consider percolation on the discrete torus $\mathbb{Z}_n^d$ at $p_c(\mathbb{Z}^d)$, the critical value for percolation on the corresponding infinite lattice $\mathbb{Z}^d$, and within the scaling window around it. We assume that $d$ is a…
We perform large scale numerical simulations of a directed version of the two-state stochastic sandpile model. Numerical results show that this stochastic model defines a new universality class with respect to the Abelian directed sandpile.…
The symmetry properties which determine the critical exponents and universality classes in conservative sandpile models are identified. This is done by introducing a set of models, including all possible combinations of abelian vs.…
We review the status of the two-dimensional Abelian sandpile model as a strong candidate to provide a lattice realization of logarithmic conformal invariance with central charge c=-2. Evidence supporting this view is collected from various…
We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set…
We prove that the Abelian sandpile model on a random binary and binomial tree, as introduced in \cite{rrs}, is not critical for all branching probabilities $p<1$; by estimating the tail of the annealed survival time of a random walk on the…
Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with diffusivity parameter $\kappa = 2$. In this paper we consider the dissipative ASM and…
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 study the sandpile model in infinite volume on $\mathbb{Z}^d$. In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure $\mu$, are $\mu$-almost surely stabilizable.…
The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different…
A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model…
The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law, $D(n)\sim n^{-\xi}$, for large avalanches. The exponent $\xi$ depends upon how the avalanches are provoked. While it is known that…
We consider a broad class of dependent site-percolation models on $\mathbb{Z}^d$ obtained by applying a monotone automaton to a random initial particle configuration drawn from a stochastically increasing family of measures. We prove that…
We study the Abelian sandpile model (ASM), a process where grains of sand are placed on a graph's vertices. When the number of grains on a vertex is at least its degree, one grain is distributed to each neighboring vertex. This model has…
The Abelian Sandpile Model is a discrete diffusion process defined on graphs (Dhar \cite{DD90}, Dhar et al. \cite{DD95}) which serves as the standard model of \textit{self-organized criticality}. The transience class of a sandpile is…
Consider the convex hull of a collection of disjoint open discs with radii $1/2$. The boundary of the convex hull consists of a finite number of line segments and arcs. Randomly choose a point in one of the arcs in the boundary so that the…
We study numerically the dynamical properties of the BTW model on a square lattice for various dimensions. The aim of this investigation is to determine the value of the upper critical dimension where the avalanche distributions are…
It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It…