# PublicationsManuscripts

## Two proofs of the central limit theorem

Yuval Filmus

We provide two proofs of the central limit theorem (up to Lévy’s continuity theorem), one using cumulants and the other using moments. As a bonus, we also prove the asymptotic normality of the number of distinct prime factors of a ‘random’ integer. Our account follows the exposition in the book The semicircle law, free random variables and entropy.

This talk was given at the Toronto Student Seminar on 20/1/2010.