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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Recurrence Function on Sturmian Words: A Probabilistic Study
verfasst von : Valérie Berthé, Eda Cesaratto, Pablo Rotondo, Brigitte Vallée, Alfredo Viola
Erschienen in: Mathematical Foundations of Computer Science 2015
Verlag: Springer Berlin Heidelberg
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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.