On strong and almost sure local limit theorems for a probabilistic model of the Dickman distribution

Régis de la Bretèche, Gérald Tenenbaum

Let $\{Z_k{\}}_{k⩾1}$ denote a sequence of independent Bernoulli random variables defined by $\mathbb{P}(Z_k=1)=1/k=1-\mathbb{P}(Z_k=0)$ $(k⩾1)$ and put $T_n:=\su…