Abstract
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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Berthé, V., Cesaratto, E., Rotondo, P., Vallée, B., Viola, A. (2015). Recurrence Function on Sturmian Words: A Probabilistic Study. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48057-1_9
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DOI: https://doi.org/10.1007/978-3-662-48057-1_9
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