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...

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

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

University of Cologne. He is known in particular for his work on percolation theory, cellular automata and computational physics. Stauffer was born in...

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

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

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

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

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

British mathematician whose research is in probability theory. His work on percolation theory won him the Rollo Davidson Prize in 2019 and the 2024 EMS...

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

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

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

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

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...

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

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

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

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

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...

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

{\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...

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

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

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...

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

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