A Quantification of the Fourth Moment Theorem for Cyclotomic Generating Functions

Explore a mathematical lecture on the quantification of the Fourth Moment Theorem for cyclotomic generating functions. Delve into sequences of random variables Xn with values in {0, ..., n} and their probability generating functions as polynomials of degree n. Examine the unified approach to establishing quantitative normal approximation bounds for Xn, considering cases where polynomial roots are either all real or lie on the unit circle in the complex plane. Learn how the real-rooted case involves only variances of Xn, while the cyclotomic case incorporates fourth cumulants or moments. Understand the elementary proofs based on the Stein-Tikhomirov method in this 26-minute talk by Benedikt Rednoß from the Hausdorff Center for Mathematics, presented in collaboration with Christoph Thäle.