Related papers: Recursive Percolation
The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate…
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…
Consider subcritical Bernoulli bond percolation with fixed parameter p<p_c. We define a dependent site percolation model by the following procedure: for each bond cluster, we colour all vertices in the cluster black with probability r and…
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…
We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as…
We study the percolation of FINITE-SIZED objects on two- and three-dimensional lattices. Our motivation stems, on one hand from some recent interesting experimental results on transport properties of impurity-doped oxide perovskites and on…
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at or near critical external fields. The incipient infinite cluster (IIC) measure in the sense of Kesten is constructed. As a…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it…
We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with…
We study a supposed model for branched polymers which was shown in two dimensions to be in the universality class of ordinary percolation. We confirm this by high statistics simulations and show that it is in the percolation universality…
We investigate variations of the well-known Achlioptas percolation problem, which uses the method of probing sites when building up a lattice system, or probing links when building a network, ultimately resulting in the delay of the…
We study $N$-cluster correlation functions in four- and five-dimensional (4D, 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E {\bf 72}, 016126 (2005)]…
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…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…
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…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
We study critical percolation on a regular planar lattice. Let $E_G(n)$ be the expected number of open clusters intersecting or hitting the line segment $[0,n]$. (For the subscript $G$ we either take $\mathbb{H}$, when we restrict to the…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…