Euclidean algorithms are Gaussian

Viviane Baladi; Brigitte Vallee

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Euclidean algorithms are Gaussian

Viviane Baladi·Brigitte Vallee

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Abstract

This study provides new results about the probabilistic behaviour of a class of Euclidean algorithms: the asymptotic distribution of a whole class of cost-parameters associated to these algorithms is normal. For the cost corresponding to the number of steps Hensley already has proved a Local Limit Theorem; we give a new proof, and extend his result to other euclidean algorithms and to a large class of digit costs, obtaining a faster, optimal, rate of convergence. The paper is based on the dynamical systems methodology, and the main tool is the transfer operator. In particular, we use recent results of Dolgopyat.

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BibTeX RIS

Viviane Baladi, Brigitte Vallee. 2004-05-05. Euclidean algorithms are Gaussian. https://arxiv.org/abs/cs/0307062

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