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...

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

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

Master equation Partition function (mathematics) Quantum probability Percolation theory Schramm–Loewner evolution List of textbooks in thermodynamics and...

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

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

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

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

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

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

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

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

grows very large. Percolation theory characterizes the connectedness of random graphs, especially infinitely large ones. Percolation is related to the...

{\displaystyle p_{c}} . In percolation theory this cluster is named the percolating cluster. This phenomenon is quantified in percolation theory by a number of quantities...

directed percolation is illustrated to the right. In isotropic percolation a spreading agent (e.g. water) introduced at a particular site percolates along...

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

Percolation surface critical behavior concerns the influence of surfaces on the critical behavior of percolation. Percolation is the study of connectivity...

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

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

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

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...

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...

model based on percolation theory. Colonization efforts may not occur as an unstoppable rush, but rather as an uneven tendency to "percolate" outwards, within...

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

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

processes, stochastic geometry, spatial statistics and continuum percolation theory. The point process depends on a single mathematical object, which...

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

growth technique Percolation theory – Mathematical theory on behavior of connected clusters in a random graph Continuum percolation theory Superfluid film –...

fields such as stochastic geometry, spatial statistics and continuum percolation theory and frequently serve as mathematical models of random phenomena, representable...