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.
CITATION STYLE
BerthÉ, V., Cesaratto, E., Rotondo, P., Vallée, B., & Viola, A. (2015). Recurrence function on Sturmian words: A probabilistic study. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9234, pp. 116–128). Springer Verlag. https://doi.org/10.1007/978-3-662-48057-1_9
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