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We consider a Markov chain obtained by random iterations of Lipschitz maps$T_i$ chosen with a probability $p_i(x)$ depending on the current position $x$.We assume this system has a property of "contraction on average", that is$\sum_i d(T_ix,T_iy)p_i(x) < \rho d(x,y)$ for some $\rho<1$. In the presentnote, we study the weak convergence of the empirical process associated to thisMarkov chain.

Empirical processes of iterated maps that contract on average