Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

@article{Kloeckner2014ContractionIT,
  title={Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps},
  author={Beno{\^i}t R. Kloeckner and Artur O. Lopes and Manuel Stadlbauer},
  journal={arXiv: Dynamical Systems},
  year={2014}
}
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke) inequality. Our main result is the following. Suppose $T$ is an expanding transformation acting on a compact metric space $M$ and $A: M \to \mathbb{R}$ a given fixed H{\"o}lder function, and denote by $L$ the Ruelle operator associated to $A$. We show that if $L$ is… 
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