- Series
- Stochastics Seminar
- Time
- Thursday, November 14, 2019 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Marcus Michelen – University of Illinois, Chicago – marcusmi@sas.upenn.edu – https://www.math.upenn.edu/~marcusmi/
- Organizer
- Michael Damron
Let X be a random variable taking values in {0,...,n} and f(z) be its probability generating function. Pemantle conjectured that if the variance of X is large and f has no roots close to 1 in the complex plane, then X must be approximately normal. We will discuss a complete resolution of this conjecture in a strong quantitative form, thereby giving the best possible version of a result of Lebowitz, Pittel, Ruelle and Speer. Additionally, if f has no roots with small argument, then X must be approximately normal, again in a sharp quantitative form. These results also imply a multivariate central limit theorem that answers a conjecture and completes a program of Ghosh, Liggett and Pemantle. This talk is based on joint work with Julian Sahasrabudhe.