Iterated Random Functions

@article{Diaconis1999IteratedRF,
  title={Iterated Random Functions},
  author={Persi Diaconis and David Freedman},
  journal={SIAM Review},
  year={1999},
  volume={41},
  pages={45-76}
}
A bstract. 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. 
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