Marcus Michelen, University of Illinois, Chicago

Abstract

The multivariate central limit theorem yields a solution to a question of Behrouzi-Far and Zeilberger concerning the average maximal number of balls in a bin. An overview of the classical central limit theorem---both the univariate and multivariate version---will be presented along with the solution to the balls and bin problem as a worked example. Time permitting, recent work joint with Julian Sahasrabudhe will be discussed, in which we show that central limit theorems follow from zero-free regions of generating functions. No knowledge of probability theory will be assumed.