Sur le biais d'une loi de probabilité relative aux entiers friables

Abstract

The standard probability law on the set $S(x,y)$ of $y$-friable integers not exceeding $x$ assigns to each friable integer $n$ a probability proportional to $1/n^{\alpha }$ where $\alpha =\alpha (x,y)$ is the saddle-point of the inverse Laplace integral for $\Psi (x,y):=|S(x,y)|$. This law presents a structural bias inasmuch it weights integers $>x$. We propose a quantitative measure of this bias and exhibit a related Gaussian distribution.

in French