Large deviations for denominators of continued fractions

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We give exponential upper bounds on the probability with which the denominator of the nth convergent in the regular continued fraction expansion stays away from the mean 12nlogπ22. The exponential rate is best possible, given by an analytic function related to the dimension spectrum of Lyapunov exponents for the Gauss transformation. We also establish the large deviation principle (LDP) for denominators. As corollaries, we derive the LDPs for denominators of periodic continued fractions and continued fraction preimages. Proofs of the main results rely on the thermodynamic formalism for finite topological Markov shifts.

本文言語English
ページ(範囲)5861-5874
ページ数14
ジャーナルNonlinearity
33
11
DOI
出版ステータスPublished - 2020 11

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)
  • 応用数学

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