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arXiv · 1610.01479

The recurrence function of a random Sturmian word

Pablo Rotondo·Brigitte Vallee
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Abstract

This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian word. This parameter is central to combinatorics of words. Having fixed a possible length $n$ for the factors, we let $\alpha$ to be drawn uniformly from the unit interval $[0,1]$, thus defining a random Sturmian word of slope $\alpha$. Thus the waiting time for these factors becomes a random variable, for which we study the limit distribution and the limit density.

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Pablo Rotondo, Brigitte Vallee. 2016-10-05. The recurrence function of a random Sturmian word. https://arxiv.org/abs/1610.01479

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