Statistical limit laws for hyperbolic groups

Cantrell, Stephen

doi:10.1090/tran/8266

Statistical limit laws for hyperbolic groups

Author: Stephen Cantrell
Journal: Trans. Amer. Math. Soc. 374 (2021), 2687-2732
MSC (2020): Primary 37D40; Secondary 20F10, 20F67, 20F65
DOI: https://doi.org/10.1090/tran/8266
Published electronically: December 18, 2020
MathSciNet review: 4223030
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Abstract: Using techniques from ergodic theory and symbolic dynamics, we derive statistical limit laws for real valued functions on hyperbolic groups. In particular, our results apply to convex cocompact group actions on $\text {CAT}(-1)$ spaces, and provide a precise statistical comparison between word length and displacement. After generalising our methods to the multidimensional setting, we prove that the abelianisation map satisfies a non-degenerate multidimensional central limit theorem. We also obtain local limit theorems for group homomorphisms and for the displacement function associated to certain actions.

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