Editing Percolation (section)

==Background==
During the last decades, [[percolation theory]], the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, [[complex network]]s, [[epidemiology]], and other fields. For example, in [[geology]], percolation refers to filtration of water through soil and permeable rocks. The water flows to [[groundwater recharge|recharge]] the [[groundwater]] in the [[water table]] and [[aquifer]]s. In places where [[infiltration basin]]s or [[septic drain field]]s are planned to dispose of substantial amounts of water, a [[percolation test]] is needed beforehand to determine whether the intended structure is  likely to succeed or fail.
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 (dynamical systems)|universality]]. [[Statistical physics]] concepts such as scaling theory, [[renormalization]], [[phase transition]], [[critical phenomena]] and [[fractal]]s are used to characterize percolation properties.
[[Combinatorics]] is commonly employed to study [[percolation threshold]]s.

Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used.  The current fastest algorithm for percolation was published in 2000 by [[Mark Newman]] and Robert Ziff.<ref name="newman">{{cite journal |last1=Newman |first1=Mark |author-link=Mark Newman |last2=Ziff |first2=Robert |title=Efficient Monte Carlo Algorithm and High-Precision Results for Percolation |journal=[[Physical Review Letters]] |volume=85 |issue=19 |pages=4104–4107 |year=2000 |doi=10.1103/PhysRevLett.85.4104 |pmid=11056635 |arxiv=cond-mat/0005264 |bibcode=2000PhRvL..85.4104N |citeseerx=10.1.1.310.4632 |s2cid=747665 }}</ref>