A Symmetric Random Walk defined by the Time-One Map of a Geodesic Flow

Pablo D. Carrasco; Túlio Vales

A Symmetric Random Walk defined by the Time-One Map of a Geodesic Flow

Dynamical Systems 2020-10-23 v3

Authors: Pablo D. Carrasco , Túlio Vales

Abstract

In this note we consider a symmetric random walk defined by a $(f,f^{-1})$ Kalikow type system, where $f$ is the time-one map of the geodesic flow corresponding to an hyperbolic manifold. We provide necessary and sufficient conditions for the existence of an stationary measure for the walk that is equivalent to the volume in the corresponding unit tangent bundle. Some dynamical consequences for the random walk are deduced in these cases.

Keywords

symmetric random walk kalikow system geodesic flow hyperbolic manifold stationary measure unit tangent bundle

Cite

@article{arxiv.2007.11558,
  title  = {A Symmetric Random Walk defined by the Time-One Map of a Geodesic Flow},
  author = {Pablo D. Carrasco and Túlio Vales},
  journal= {arXiv preprint arXiv:2007.11558},
  year   = {2020}
}

Comments

Final version incorporating the reviewer suggestions. To be published in Discrete and Continuous Dynamical Systems. 18 pages, 1 fig

A Symmetric Random Walk defined by the Time-One Map of a Geodesic Flow

Abstract

Keywords

Cite

Comments

Related papers