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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.
In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few active neighbors are successively removed from the active set until the system stabilizes. The order in which this removal occurs makes no difference ...
Pages in category "Percolation theory" The following 13 pages are in this category, out of 13 total. ... About Wikipedia; Disclaimers; Contact Wikipedia; Code of Conduct;
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.
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.
Duminil-Copin and Smirnov used percolation theory and the vertices and edges connecting them in a lattice to model fluid flow and with it phase transitions. The pair investigated the number of self-avoiding walks that were possible in hexagonal lattices, connecting combinatorics to percolation theory.
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.