Probability Seminars

## 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.

- Speaker: Julian Sahasrabudhe (Cambridge)
- Tuesday 12 November 2019, 15:15–16:15
- Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
- Series: Probability; organiser: Perla Sousi.