Title: Iterated Random Functions
Authors: Persi Diaconis and David Freedman 
Date: 1 March 1998
Pub: PDF
Url: http://www.stat.berkeley.edu/~census/511.pdf
Abstract:
Iterated random functions are used to draw pictures or simulate
large Ising models, among other applications.  Random iterations
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.