We obtain a central limit theorem for a general class of additive parameters (costs,
observables) associated to three standard Euclidean algorithms, with optimal speed of …

We consider a one-parameter family of expanding interval maps $\{T_ {\alpha}\} _ {\alpha\in
[0, 1]} $(japanese continued fractions) which include the Gauss map ($\alpha= 1$) and the …

We study a general class of Euclidean algorithms which compute the greatest common
divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an …

We construct a countable family of open intervals contained in (0, 1] whose endpoints are
quadratic surds and such that their union is a full measure set. We then show that these …

We study a two-parameter family of one-dimensional maps and related (a, b)-continued
fractions suggested for consideration by Don Zagier. We prove that the associated natural …

The entropy $ h (T_\alpha) $ of $\alpha $-continued fraction transformations is known to be
locally monotone outside a closed, totally disconnected set $\EE $. We will exploit the …

We estimate density and regression functions for weak dependent data. Using an
exponential inequality obtained by Dedecker and Prieur (New dependence coefficients …

Two closely related families of α-continued fractions were introduced in 1981: by Nakada on
the one hand, by Tanaka and Ito on the other hand. The behavior of the entropy as a …

In pattern matching algorithms, a characteristic parameter is the number of occurrences of a
given pattern in a random text of length n generated by a source. We consider here a …

The Gaussian algorithm for lattice reduction in dimension 2 is precisely analysed under a
class of realistic probabilistic models, which are of interest when applying the Gauss …