Related papers: Anisotropy in finite continuum percolation: Thresh…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…
Scaling theory, duality symmetry, and numerical simulations of a random network model are used to study the magnetoresistance of a metal/insulator/perfect conductor composite with a disordered columnar microstructure. The phase diagram is…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
We consider the Boolean model $Z$ on $\mathbb{R}^d$ with random compact grains, i.e. $Z := \bigcup_{i \in \mathbb{N}} (X_i + Z_i)$ where $\eta_t := \{X_1, X_2, \dots\}$ is a Poisson point process of intensity $t$ and $(Z_1, Z_2, \dots)$ is…
We study the crossover from self--similar scaling behavior to asymptotically self--affine (anisotropic) structures. As an example, we consider bond percolation with one preferred direction. Our theory is based on a field--theoretical…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We study percolation problems of overlapping objects where the underlying geometry is such that in D-dimensions, a subset of the directions has a lattice structure, while the remaining directions have a continuum structure. The resulting…
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…
In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation…
The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the…
We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with $\mathbb{Z}$, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent…
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
We investigate percolation in mixtures of nanorods in the presence of external fields that align or disalign the particles with the field axis. Such conditions are found in the formulation and processing of nanocomposites, where the field…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using…