Related papers: Anisotropic oriented percolation in high dimension…
According to the scaling theory of localization, all quantum electronic states are localized in two-dimensional (2D) systems. One consequence of the theory is that there is no quantum percolation transition in 2D. However, in a real system…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
The general epidemic process is a paradigmatic model in non-equilibrium statistical physics displaying a continuous phase transition between active and absorbing states.The dynamic isotropic percolation universality class captures its…
We study a dynamical model of a rod-like particle surrounded by a cloud of smaller particles of the same charge and we show that, in the presence of a low-frequency alternating electric field, the rod displays the same type of anomalous…
The one-dimensional kinetic contact process with parallel update is introduced and studied by the mean-field approximation and Monte Carlo (MC) simulations. Contrary to a more conventional scenario with single active phase for 1d models…
We have generalized the idea of backbend in a nearest-neighbor oriented bond percolation process by considering a backbend sequence $\beta : \mathbb{Z}_+ \to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $\beta$-backbend path from the…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
We introduce the notion of \emph{localization at the boundary} for conditioned random walks in i.i.d. and uniformly elliptic random environment on $\mathbb{Z}^d$, in dimensions two and higher. Informally, this means that the walk spends a…
The influence of a local anisotropy of random orientation on a ferromagnetic phase transition is studied for two cases of anisotropy axis distribution. To this end a model of a random anisotropy magnet is analyzed by means of the field…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
We prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on Z^d. That is, for each d at least 2, and for any supercritical parameter p > p_c, we prove the existence of a…
A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a…
We consider the bond percolation model on the lattice $\mathbb{Z}^d$ ($d\ge 2$) with the constraint to be fully connected. Each edge is open with probability $p\in(0,1)$, closed with probability $1-p$ and then the process is conditioned to…
In this paper we study Poisson processes of so-called "fat" cylinders in hyperbolic space. As our main result we show that this model undergoes a percolation phase transition. We prove this by establishing a novel link between the fat…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $\mathbb Z^d$ in powers of $d^{-1}$ as $d\rightarrow \infty$. The proof relies heavily on the lace expansion.
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques, we transform the problem to a particular…
We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a three-fold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow…
The site percolation problem is studied on d-dimensional generalisations of the Kagome' lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site…