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 weight proportional to 1/n α , where α=α(x,y) is the saddle-point of the inverse Laplace integral for Ψ(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.