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We study Markov chains generated by iterated Lipschitz functions systems withpossibly place dependent probabilities. Under general conditions, we proveuniqueness of the invariant probability measure for the associated Markovchain, by using quasi-compact linear operators technics. We use the sameapproach to describe the behavior of the Diaconis-Friedman's chain on [0,1]with possibly place dependent probabilities.

Iterated function systems with place dependent probabilities and application to the Diaconis-Friedman's chain on [0,1]