Bootstrap percolation is a random process that models the spread of activation on a linked structure. Starting with an initial set of active vertices, in each round all inactive vertices with at least r active neighbors become and remain active until there are no inactive vertices with enough active neighbors left. Due to its numerous applications in modeling of physical processes, bootstrap pe...

The work of Fortuin and Kasteleyn [1] demonstrated that bond percolation may be viewed as the s ~ 1 limit of the s-state Potts model. Recent interest in theories of random surfaces, particularly in the context of gauge theories [2], has led to the question of whether there is a natural generalization of the Fortuin-Kasteleyn result to plaquette percolation. It has been asserted that the proper ...

The percolation process provides a simple picture of a critical point transition and has been of increasing recent theoretical interest. We refer to several review articles (1-a~ for a general survey of the subject. An important development first established by Kasteleyn and Fortuin (4,5~ is the connection between bond percolation and a lattice statistical model. This consideration leads to a f...

The percolation theory is established as a useful tool in the field of pharmaceutical materials science. It is shown that percolation theory, developed for analyzing insulator–conductor transitions, can be applied to describe imperfect dc conduction in pharmaceutical microcrystalline cellulose during densification. The system, in fact, exactly reproduces the values of the percolation threshold ...

Site-bond percolation is addressed in a very general class of correlated sitebond systems. The site-bond model analyzed provides a simple natural picture of disordered media such as porous materials, non-uniform surfaces adsorption potential, conductivity of inhomogeneous systems and landscapes. The bond (site) percolation threshold exhibits an extraordinary behavior, showing maxima and minima ...

In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At the central stage shall be the real-space renormalization group treatment of the percolation problem. As a rather novel application of this approach to percola...

We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act independently of one another. By avoiding explicit use of microscopic paths, it is first established that the model possesses the typical attributes which are indic...

A Monte Carlo analysis of percolation of line-segments on a square lattice. Abstract We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases , goes through a minimum and then increases slowly for large segments. We explain this non-monotonic be...

The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied percolation or epidemics in clustered networks, but the networks often contain preferential contacts in high degree n...

We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on [n] with initial set A ∼ Bin([n], p). We determine T up to a constant factor with high probability for all p above the critical probability for percolation, and to within a 1 + o(1) factor for a large range of p.