Viviane Baladi, Brigitte Vallee
Euclidean algorithms are Gaussian
(756K, postscript)

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.