## Iterated random functions (1999)

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by
Persi Diaconis
,
David Freedman

Venue: | SIAM Review |

Citations: | 133 - 1 self |

### BibTeX

@ARTICLE{Diaconis99iteratedrandom,

author = {Persi Diaconis and David Freedman},

title = {Iterated random functions},

journal = {SIAM Review},

year = {1999},

volume = {41},

pages = {45--76}

}

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### Abstract

Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples. There is a simple unifying idea: the iterates of random Lipschitz functions converge if the functions are contracting on the average. 1. Introduction. The