- 03-474 Viviane Baladi, Brigitte Vallee
- Euclidean algorithms are Gaussian
Oct 24, 03
(auto. generated ps),
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.