Related papers: Convergence of threshold estimates for two-dimensi…
In this paper, the 60-year-old concept of long-range interaction in percolation problems introduced by Dalton, Domb, and Sykes, is reconsidered. With Monte Carlo simulation -- based on Newman-Ziff algorithm and finite-size scaling…
We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling…
We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs of points converges to an explicit…
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…
We examine the percolation model in $\mathbb{Z}^d$ by an approach involving lattice animals, in which their relevant characteristic is surface-area-to-volume ratio. Two critical exponents are introduced. The first is related to the growth…
By means of Monte Carlo simulations, we study long-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors, up to the eighth neighbors for the square lattice and the ninth neighbors for the…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen-Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices…
We report the critical point for site percolation for the "explosive" type for 2D square lattices using Monte Carlo simulations and compare it to the classical well known percolation. We use similar algorithms as have been recently reported…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
We use a large cell Monte Carlo Renormalization procedure, to compute the critical exponents of a system of growing linear polymers. We simulate the growth of non-intersecting chains in large MC cells. Dense regions where chains get in each…
In this work, we present a new algorithm to approximate the percolation centrality of every node in a graph. Such a centrality measure quantifies the importance of the vertices in a network during a contagious process. In this paper, we…
Percolation for a planar lattice has a single percolation threshold, whereas percolation for a negatively curved lattice displays two separate thresholds. The enhanced binary tree (EBT) can be viewed as a prototype model displaying two…
For the site percolation model on the triangular lattice and certain generalizations for which Cardy's Formula has been established we acquire a power law estimate for the \emph{rate} of convergence of the crossing probabilities to Cardy's…
It is known that the number of points in the largest cluster of a percolating Poisson process restricted to a large finite box is asymptotically normal. In this note, we establish a rate of convergence for the statement. As each point in…
We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical…
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…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
We present a coupled decreasing sequence of random walks on $ \mathbb Z $ that dominates the edge process of oriented-bond percolation in two dimensions. Using the concept of "random walk in a strip ", we construct an algorithm that…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…