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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Statistical limit laws for hyperbolic groups
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by Stephen Cantrell PDF
Trans. Amer. Math. Soc. 374 (2021), 2687-2732 Request permission


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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Additional Information
  • Stephen Cantrell
  • Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
  • Email:
  • Received by editor(s): June 3, 2019
  • Received by editor(s) in revised form: April 20, 2020, April 27, 2020, June 24, 2020, and July 20, 2020
  • Published electronically: December 18, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 2687-2732
  • MSC (2020): Primary 37D40; Secondary 20F10, 20F67, 20F65
  • DOI:
  • MathSciNet review: 4223030