Dimitris Koukoulopoulos: Factoring Random Integers (September 10, 2025)

Billingsley proved that the prime factors of a random integer are known to follow the Poisson–Dirichlet distribution of parameter 1. Arratia gave a new proof of this result by constructing a coupling between the prime factors of a random integer and a Poisson–Dirichlet distribution. His proof furnished a quantitative version of Billingsley’s theorem, which he conjectured could be improved. In this talk, Dimitris Koukoulopoulos will present recent work with Tony Haddad, where we proved Arratia’s conjecture. Furthermore, Koukoulopoulos will explain how to use these methods to deduce various other results about the distribution of divisors of integers. Uploaded 25-09-25 For more information go here: https://www.simonsfoundation.org/event/mps-conference-on-universal-statistics-in-number-theory/