14:00
Let $X$ be a random variable, taking values in $\{1,…,n\}$, with standard deviation $\sigma$ and let $f_X$ be its probability generating function. Pemantle conjectured that if $\sigma$ 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. As an application, we resolve a conjecture of Ghosh, Liggett and Pemantle by proving a multivariate central limit theorem for, so called, strong Rayleigh distributions. I will also discuss how these sorts of results shed light on random variables that arise naturally in combinatorial settings. This talk is based on joint work with Marcus Michelen.
Further Information
Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.