Editing Random walk (section)

===Self-interacting random walks===
There are a number of interesting models of random paths in which each step depends on the past in a complicated manner. All are more complex for solving analytically than the usual random walk; still, the behavior of any model of a random walker is obtainable using computers. Examples include:
* The [[self-avoiding walk]].<ref>Madras, Neal and Slade, Gordon (1996) ''The Self-Avoiding Walk'', Birkhäuser Boston. {{isbn|0-8176-3891-1}}.</ref>
The self-avoiding walk of length ''n'' on <math>\mathbb{Z}^d</math> is the random ''n''-step path which starts at the origin, makes transitions only between adjacent sites in <math>\mathbb{Z}^d</math>, never revisit a site, and is chosen uniformly among all such paths. In two dimensions, due to self-trapping, a typical self-avoiding walk is very short,<ref>{{cite journal|author1=Hemmer, S. |author2=Hemmer, P. C. |title=An average self-avoiding random walk on the square lattice lasts 71 steps|journal=J. Chem. Phys.| volume=81|issue=1 | pages=584–585| year=1984| doi=10.1063/1.447349|bibcode = 1984JChPh..81..584H |doi-access=free}}</ref> while in higher dimension it grows beyond all bounds.
This model has often been used in [[polymer physics]] (since the 1960s).
* The [[loop-erased random walk]].<ref>Lawler, Gregory (1996). ''Intersection of random walks'', Birkhäuser Boston. {{isbn|0-8176-3892-X}}.</ref><ref>Lawler, Gregory ''Conformally Invariant Processes in the Plane'', [http://www.math.cornell.edu/~lawler/book.ps book.ps].</ref>
* The [[reinforced random walk]].<ref>{{cite journal|author=Pemantle, Robin |year=2007|url=http://www.emis.de/journals/PS/images/getdoc9b04.pdf?id=432&article=94&mode=pdf |title=A survey of random processes with reinforcement|journal= Probability Surveys|volume =4 |pages=1–79|arxiv=math/0610076|doi=10.1214/07-PS094|s2cid=11964062}}</ref>
* The [[exploration process]].{{citation needed|date=April 2012}}
* The [[multiagent random walk]].<ref>Alamgir, M. and [[Ulrike von Luxburg|von Luxburg, U.]] (2010). [http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/AlamgirLuxburg2010_%5b0%5d.pdf "Multi-agent random walks for local clustering on graphs"] {{Webarchive|url=https://web.archive.org/web/20120415052311/http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/AlamgirLuxburg2010_%5b0%5d.pdf |date=15 April 2012 }}, ''IEEE 10th International Conference on Data Mining (ICDM)'', pp. 18–27.</ref>
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