Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces

  title={Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces},
  author={A. Naor and Y. Peres and O. Schramm and S. Sheffield},
  journal={Duke Mathematical Journal},
  • A. Naor, Y. Peres, +1 author S. Sheffield
  • Published 2004
  • Mathematics
  • Duke Mathematical Journal
  • A metric space X has Markov type 2, if for any reversible flnite-state Markov chain fZtg (with Z0 chosen according to the stationary distribution) and any map f from the state space to X, the distance Dt from f(Z0) to f(Zt) satisfles E(D 2) • K 2 tE(D 2) for some K = K(X) 2) has Markov type 2; this proves a conjecture of Ball. We also show that trees, hyperbolic groups and simply connected Riemannian manifolds of pinched negative curvature have Markov type 2. Our results are applied to settle… CONTINUE READING
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