  We investigate the transportation cost-information inequalities for
bifurcating Markov chains which are a class of processes indexed by binary
tree. These processes provide models for cell growth when each individual in
one generation gives birth to two offsprings in the next one. Transportation
cost inequalities provide useful concentra-tion inequalities. We also study
deviation inequalities for the empiri-cal means under relaxed assumptions on
the Wasserstein contraction of the Markov kernels. Applications to bifurcating
non linear autore-gressive processes are considered: deviation inequalities for
pointwise estimates of the non linear leading functions.
