Related papers: Iterative Site Percolation on Triangular Lattice
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in…
In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last…
We construct the uniform infinite planar map (UIPM), obtained as the n \to \infty local limit of planar maps with n edges, chosen uniformly at random. We then describe how the UIPM can be sampled using a "peeling" process, in a similar way…
Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…
In conventional site percolation, all lattice sites are occupied with the same probability. For a bipartite lattice, sublattice-selective percolation instead involves two independent occupation probabilities, depending on the sublattice to…
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent…
The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we construct the IIC measure for high-dimensional percolation models…
We define an inhomogeneous percolation model on "ladder graphs" obtained as direct products of an arbitrary graph $G = (V,E)$ and the set of integers $\mathbb{Z}$ (vertices are thought of as having a "vertical" component indexed by an…
Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation…
In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the…
We consider critical percolation on the triangular lattice in a bounded simply connected domain with boundary conditions that force an interface between two prescribed boundary points. We say the interface forms a "near-loop" when it comes…
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…