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Conference Papers Year : 2015

Recurrence Function on Sturmian Words: A Probabilistic Study

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 α, we associate particular sequences of factor lengths which have a given “position” with respect to the sequence of continuants of α, we then let α 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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Dates and versions

hal-01199096 , version 1 (14-09-2015)

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Valérie Berthé, Eda Cesaratto, Pablo Rotondo, Brigitte Vallée, Alfredo Viola. Recurrence Function on Sturmian Words: A Probabilistic Study. Mathematical Foundations of Computer Science 2015 - 40th International Symposium, MFCS 2015, Aug 2015, Milan, Italy. pp.116-128, ⟨10.1007/978-3-662-48057-1_9⟩. ⟨hal-01199096⟩
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