Extensions of Billingsley's Theorem via Multi-Intensities

Richard Arratia, Fred Kochman, Victor S. Miller

Let $p_1\ge p_2\ge \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$, and let $$\frac{\log p_1}{\log n},\frac{\log p_2}{\log n},\dots$$ be the…