Random walks of infinite moment on free semigroups

Abstract

We consider random walks on finitely or countably generated free semigroups, and identify their Poisson boundaries for classes of measures which fail to meet the classical entropy criteria, namely measures with infinite entropy or infinite logarithmic moment.

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Acknowledgements

We would like to thank Lewis Bowen, Vadim Kaimanovich, and Joseph Maher for fruitful discussions. G. T. is partially supported by NSERC and the Alfred P. Sloan Foundation.

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Correspondence to Giulio Tiozzo.

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Forghani, B., Tiozzo, G. Random walks of infinite moment on free semigroups. Probab. Theory Relat. Fields 175, 1099–1122 (2019). https://doi.org/10.1007/s00440-019-00911-7

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Keywords

  • Random walks
  • Poisson boundary
  • Free semigroups
  • Free groups

Mathematics Subject Classification

  • 60G50
  • 60J50
  • 05C81