Related papers: Bond percolation does not simulate site percolatio…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
The question of how clustering (non-zero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modelling highly-clustered networks are employed…
In this paper we study anisotropic oriented percolation on $\mathbb{Z}^d$ for $d\geq 4$ and show that the local condition for phase transition is closely related to the mean-field condition. More precisely, we show that if the sum of the…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses $k \ge 1$ incident edges, whose weight is then increased by 1. The choice of this $k$-tuple occurs…
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…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
We propose a simulation model to study the properties of directed percolation in two-dimensional (2D) anisotropic random media. The degree of anisotropy in the model is given by the ratio $\mu$ between the axes of a semi-ellipse enclosing…
Percolation on a five-dimensional simple hypercubic (sc(5)) lattice with extended neighborhoods is investigated by means of extensive Monte Carlo simulations, using an effective single-cluster growth algorithm. The critical exponents,…
We study bond percolation in $\mathbb{Z}^d$ with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs in this model if and only if percolation also occurs in the…
In this article, we revisit random site and bond percolation in square lattice focusing primarily on the behavior of entropy and order parameter. In the case of traditional site percolation, we find that both the quantities are zero at…
In 1991 Aizenman and Grimmett claimed that any `essential enhancement' of site or bond percolation on a lattice lowers the critical probability, an important result with many implications, such as strict inequalities between critical…
The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model…
In this note we discuss vacant set level set percolation on a transient weighted graph. It interpolates between the percolation of the vacant set of random interlacements and the level set percolation of the Gaussian free field. We employ…
We consider the supercritical finite-range random connection model where the points $x,y$ of a homogeneous planar Poisson process are connected with probability $f(|y-x|)$ for a given $f$. Performing percolation on the resulting graph, we…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
We prove a nonuniqueness theorem for Bernoulli site percolation on properly embedded planar graphs, and we obtain a general connectivity principle beyond planarity. Let $G$ be an infinite connected graph properly embedded in $\RR^2$ with…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…