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Random walks on random coset spaces with applications to Furstenberg entropy

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Abstract

We determine the range of Furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces.

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Acknowledgements

I’d like to thank Amos Nevo for asking me whether Theorem 1.1 is true and for several motivating discussions and Yuri Lima, Yair Hartman and Omer Tamuz for discovering an error in a previous version. I’d also like to thank the anonymous referees for their careful readings and helpful criticism.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-1372, USA

    Lewis Bowen

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  1. Lewis Bowen
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Correspondence to Lewis Bowen.

Additional information

Research supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274.

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Bowen, L. Random walks on random coset spaces with applications to Furstenberg entropy. Invent. math. 196, 485–510 (2014). https://doi.org/10.1007/s00222-013-0473-0

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