On the rate of mixing of circle extensions of Anosov maps
  We study circle extensions of analytic Anosov maps on the two torus: these are examples of partially hyperbolic maps for which the qualitative ergodic theory is well understood. In this paper we investigate rates of mixing (for the SRB measure) and prove explicit lower bounds involving the topological pressure of two times the unstable Jacobian. In particular we study the case when the extension function ("roof function") is given by a random trigonometric polynomial. 
Fr\'ed\'eric Naud
math.DS