Recurrence Function on Sturmian Words: A Probabilistic Study

  • Valérie Berthé
  • Eda Cesaratto
  • Pablo Rotondo
  • Brigitte Vallée
  • Alfredo Viola
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)


This paper is a first attempt to describe the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which provides precise information on the structure of such a word. With each Sturmian word of slope \(\alpha \), we associate particular sequences of factor lengths which have a given “position” with respect to the sequence of continuants of \(\alpha \), we then let \(\alpha \) to be uniformly drawn inside the unit interval [0,1]. This probabilistic model is well-adapted to better understand the role of the position in the recurrence properties.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Valérie Berthé
    • 1
  • Eda Cesaratto
    • 2
  • Pablo Rotondo
    • 3
  • Brigitte Vallée
    • 4
  • Alfredo Viola
    • 3
  1. 1.LIAFA, CNRS UMR 7089University Paris DiderotParisFrance
  2. 2.Conicet and Universidad Nacional de General SarmientoBuenos AiresArgentina
  3. 3.Universidad de la RepúblicaMontevideoUruguay
  4. 4.GREYC, CNRS UMR 6072University de CaenCaenFrance

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