Editing Random walk (section)

{{Short description|Process forming a path from many random steps}}
{{for|the novel|Random Walk}}
{{Use dmy dates|date=March 2020}}
{{Probability fundamentals}}

[[File:Eight-step random walks.png|thumb|Five eight-step random walks from a central point. Some paths appear shorter than eight steps where the route has doubled back on itself. ([[:File:Random_Walk_Simulator.gif|animated version]])]]

In [[mathematics]], a '''random walk''', sometimes known as a '''drunkard's walk''', is a [[stochastic process]] that describes a path that consists of a succession of [[random]] steps on some [[Space (mathematics)|mathematical space]].

An elementary example of a random walk is the random walk on the integer number line <math>\mathbb Z</math> which starts at 0, and at each step moves +1 or −1 with equal [[probability]]. Other examples include the path traced by a [[molecule]] as it travels in a liquid or a gas (see [[Brownian motion]]), the search path of a [[foraging]] animal, or the price of a fluctuating [[random walk hypothesis|stock]] and the financial status of a [[gambler]]. Random walks have applications to [[engineering]] and many scientific fields including [[ecology]], [[psychology]], [[computer science]], [[physics]], [[chemistry]], [[biology]], [[economics]], and [[sociology]]. The term ''random walk'' was first introduced by [[Karl Pearson]] in 1905.<ref>{{cite journal| last=Pearson | first=Karl |title=The Problem of the Random Walk|journal=Nature|volume=72|issue=1865|page=294 |doi=10.1038/072294b0| year=1905 | bibcode=1905Natur..72..294P|s2cid=4010776}}</ref>

Realizations of random walks can be obtained by [[Monte Carlo Simulation|Monte Carlo simulation]].<ref>Theory and Applications of Monte Carlo Simulations.&nbsp;(2013).&nbsp;Kroatien:&nbsp;IntechOpen. Page 229, https://books.google.com/books?id=3HWfDwAAQBAJ&pg=PA229</ref>