preprint · Discrete and Continuous Dynamical Systems · 2020

A symmetric Random Walk defined by the time-one map of a geodesic flow

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Abstract

<p style='text-indent:20px;'>In this note we consider a symmetric Random Walk defined by a <inline-formula><tex-math id="M1">\begin{document}$ (f, f^{-1}) $\end{document}</tex-math></inline-formula> Kalikow type system, where <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula> 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.

Cite this paper

APA 7

Carrasco, P. D., & Vales, T. (2020). A symmetric Random Walk defined by the time-one map of a geodesic flow. Discrete and Continuous Dynamical Systems, 41(6), 2891–2905. https://doi.org/10.3934/dcds.2020390

MLA 9

Carrasco, Pablo D., and Túlio Vales. “A symmetric Random Walk defined by the time-one map of a geodesic flow.” Discrete and Continuous Dynamical Systems, vol. 41, no. 6, 2020, pp. 2891–905, https://doi.org/10.3934/dcds.2020390.

Chicago

Carrasco, Pablo D., and Túlio Vales. 2020. “A symmetric Random Walk defined by the time-one map of a geodesic flow.” Discrete and Continuous Dynamical Systems 41 (6): 2891–905. https://doi.org/10.3934/dcds.2020390.

Harvard

Carrasco, P.D. and Vales, T. (2020) ‘A symmetric Random Walk defined by the time-one map of a geodesic flow’, Discrete and Continuous Dynamical Systems, 41(6), pp. 2891–2905. Available at: https://doi.org/10.3934/dcds.2020390.

BibTeX

@misc{carrasco2020symmetric,
  title = {{A symmetric Random Walk defined by the time-one map of a geodesic flow}},
  author = {Carrasco, Pablo D. and Vales, Túlio},
  journal = {Discrete and Continuous Dynamical Systems},
  volume = {41},
  number = {6},
  pages = {2891--2905},
  year = {2020},
  doi = {10.3934/dcds.2020390}
}

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