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Sublinearly Morse boundary of CAT(0) admissible groups

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Published/Copyright: January 16, 2024

Abstract

We show that if ๐บ is an admissible group acting geometrically on a CAT โก ( 0 ) space ๐‘‹, then ๐บ is a hierarchically hyperbolic space and its ๐œ…-Morse boundary ( โˆ‚ ฮบ G , ฮฝ ) is a model for the Poisson boundary of ( G , ฮผ ) , where ๐œˆ is the hitting measure associated to the random walk driven by ๐œ‡.

Acknowledgements

We thank Mark Hagen and Kasra Rafi for useful conversations. The authors are grateful for the refereeโ€™s insightful and detailed critiques that have helped improve the exposition of this paper.

  1. Communicated by: Rachel Skipper

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Received: 2023-09-12
Revised: 2023-11-28
Published Online: 2024-01-16
Published in Print: 2024-07-01

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