03-474 Viviane Baladi, Brigitte Vallee

Euclidean algorithms are Gaussian (756K, postscript) Oct 24, 03

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 03-474.src( 03-474.keywords , distfinal.ps )