CENTRAL LIMIT THEOREMS AND THE GEOMETRY OF POLYNOMIALS

With Julian Sahasrabudhe (Cambridge)

CENTRAL LIMIT THEOREMS AND THE GEOMETRY OF POLYNOMIALS

Let X ∈ {0, . . . , n} be a random variable with standard deviation σ and let f_X be its probability generating function. Pemantle conjectured that if σ is large and f_X has no roots close to 1 in the complex plane then X must approximate a normal distribution. In this talk, I will discuss a complete resolution of Pemantle’s conjecture. I shall also mention a how these ideas can be used to prove a multivariate central limit theorem for strong Rayleigh distributions, thereby resolving a conjecture of Gosh, Liggett and Pemantle. This talk is based on joint work with Marcus Michelen.

Add to your calendar or Include in your list

How can mathematics help us to understand the behaviour of ants? Read more about the fanscinating work being carri… https://t.co/iCODvvxqE6 View on Twitter