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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Large deviation principles for countable Markov shifts
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by Hiroki Takahasi PDF
Trans. Amer. Math. Soc. 372 (2019), 7831-7855 Request permission

Abstract:

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong connectivity assumptions called “finite irreducibility” or “finite primitiveness”. More precisely, we assume the existence of a Gibbs state for a potential $\phi$ in the sense of Bowen, and prove the level-$2$ large deviation principles for the distribution of empirical means under the Gibbs state, as well as that of weighted periodic points and iterated preimages. The rate function is written with the pressure and the free energy associated with the potential $\phi$.
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Additional Information
  • Hiroki Takahasi
  • Affiliation: Keio Institute of Pure and Applied Sciences, Department of Mathematics, Keio University, Yokohama 223-8522, Japan
  • MR Author ID: 790386
  • Email: hiroki@math.keio.ac.jp
  • Received by editor(s): July 23, 2018
  • Received by editor(s) in revised form: February 6, 2019, and February 12, 2019
  • Published electronically: July 1, 2019
  • Additional Notes: This research was partially supported by the Grant-in-Aid for Young Scientists (A) of the JSPS 15H05435, the Grant-in-Aid for Scientific Research (B) of the JSPS 16KT0021, and the JSPS Core-to-Core Program “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7831-7855
  • MSC (2010): Primary 37A45, 37A50, 37A60, 60F10
  • DOI: https://doi.org/10.1090/tran/7829
  • MathSciNet review: 4029683