Sur la concentration de certaines fonctions additives

International audienceImproving on estimates of Erdős, Halász and Ruzsa, we provide new upper and lower bounds for the concentration function of the limit law of certain additive arithmetic functions under hypotheses involving only their average behaviour on the primes. In particular we partially confirm a conjecture of Erdős and Kátai. The upper bound is derived via a reappraisal of the method of Diamond and Rhoads, resting upon the theory of functions with bounded mean oscillation