applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive...

that modulates capacity for percolation. During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding...

underlying points of discrete percolation form types of lattices whereas the underlying points of continuum percolation are often randomly positioned...

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below...

In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents...

Obstruction theory Operator theory Order theory Percolation theory Perturbation theory Probability theory Proof theory Queue theory Ramsey theory Random matrix...

bunkbed conjecture (also spelled bunk bed conjecture) is a statement in percolation theory, a branch of mathematics that studies the behavior of connected clusters...

bootstrap Ising critical exponents Percolation critical exponents Network science Percolation theory Graph theory Hagen Kleinert and Verena Schulte-Frohlinde...

Graph theory Interdependent networks Network science Percolation Percolation theory Random graph theory of gelation Regular graph Scale free network Semilinear...

an analog of mean-field theory (this dimension is 4d for Ising or for directed percolation, and 6d for undirected percolation). Critical exponents are...

networks. Percolation is a model used to explain how neural activity is transmitted across the various connections within the brain. Percolation theory can...

mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul Erdős from the age of 14. As...

studied as a phase transition. This breakdown is studied via percolation theory. Graph theory is also widely used in sociology as a way, for example, to...

connected components are described by percolation theory. A key question in this theory is the existence of a percolation threshold, a critical probability...

mathematical proof more satisfying, but developed an interest in percolation theory, which is used in mathematical physics to address issues in statistical...

has been studied under the name of bootstrap percolation. Graph theory Network science Percolation Theory Core–periphery structure Cereceda's conjecture...

links are removed with heterogeneous weights as weighted percolation). As percolation theory has much of its roots in physics, much of the research done...

systematic study of percolation in two dimensions, reported in his book Percolation Theory for Mathematicians. His work on scaling theory and scaling relations...

paper "Percolation and Cluster Distribution. I. Cluster Multiple Labeling Technique and Critical Concentration Algorithm". Percolation theory is the study...

Flory–Stockmayer theory was the first theory investigating percolation processes. Flory–Stockmayer theory is a special case of random graph theory of gelation...

In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice...

processes, stochastic geometry, spatial statistics and continuum percolation theory. The Poisson point process can be defined on more abstract spaces...

Frosch described Reason's model in mathematical terms as a model in percolation theory, which he analyses as a Bethe lattice. The model includes active and...

the metallic component reaches the percolation threshold. The behavior of the conductivity near this percolation threshold will show a smooth change...

algebras, number theory and group theory. They also arise in applied mathematics in connection with coding theory, in percolation theory to study connectivity...

probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model...

in many diverse disciplines, including statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology...

percolation is a mathematical method used to describe the paths reachable in a random medium within a given amount of time. First passage percolation...

typical of all mean field theories, they fail to predict the properties of a multiphase medium close to the percolation threshold due to the absence...

(}\ln \pi (x)^{-1}+\ln \delta ^{-1}{\big )}} . Resistance distance Percolation theory Krackhardt E/I Ratio Jerrum & Sinclair 1988, pp. 235–244. Jerrum,...