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In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability p or "empty" (in which case its edges are removed) with probability 1 – p; the corresponding problem is called site percolation, see Fig. 2. Percolation typically exhibits universality.
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters.
Percolation (from the Latin word percolatio, meaning filtration [1]) is a theoretical model used to understand the way activation and diffusion of neural activity occurs within neural networks. [2] Percolation is a model used to explain how neural activity is transmitted across the various connections within the brain.
First passage percolation is one of the most classical areas of probability theory. It was first introduced by John Hammersley and Dominic Welsh in 1965 as a model of fluid flow in a porous media. [1] It is part of percolation theory, and classical Bernoulli percolation can be viewed as a subset of first passage percolation.
Pages in category "Percolation theory" The following 13 pages are in this category, out of 13 total. This list may not reflect recent changes. ...
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size.
In statistical physics, directed percolation (DP) refers to a class of models that mimic filtering of fluids through porous materials along a given direction, due to the effect of gravity. Varying the microscopic connectivity of the pores, these models display a phase transition from a macroscopically permeable (percolating) to an impermeable ...
As in discrete percolation, a common research focus of continuum percolation is studying the conditions of occurrence for infinite or giant components. [1] [2] Other shared concepts and analysis techniques exist in these two types of percolation theory as well as the study of random graphs and random geometric graphs.