Euclidean algorithms are Gaussian
<|reference_start|>Euclidean algorithms are Gaussian: 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.<|reference_end|>
@article{baladi2003euclidean,
    title={Euclidean algorithms are Gaussian},
    author={Viviane Baladi and Brigitte Vallee},
    journal={arXiv preprint arXiv:cs/0307062},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0307062},
    primaryClass={cs.DS cs.CC}
}