03-474 Viviane Baladi, Brigitte Vallee
Euclidean algorithms are Gaussian (756K, postscript) Oct 24, 03
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Abstract. We obtain a Central Limit Theorem for a class of costs associated to three standard Euclidean algorithms, with optimal speed of convergence. For lattice costs, we establish a Local Limit Theorem, with optimal speed of convergence. We view an algorithm as a dynamical system and combine tools imported from dynamics, such as transfer operators, with various other techniques. To obtain estimates on transfer operators when a parameter varies along vertical lines in the complex plane, we adapt techniques introduced by Dolgopyat in the context of continuous-time dynamics.

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