Quantitative Marcinkiewicz's theorem and central limit theorems: Applications to spin systems and point processes
Speaker: Trần Hoàng Sơn (NUS-Singapore)

Thời gian: 14h Thứ 5, ngày 14/10/2021

Link online https://meet.google.com/nqs-ntdh-wnz?pli=1

Abstract: In this talk, we want to introduce our recent work which could be seen as a quantitative version of the classical Marcinkiewicz's theorem. In particular, we obtain quantitative decay estimates on the Kolmogorov-Smirnov distance between a real random variable X and a Gaussian under the condition that the characteristic function does not vanish only on a bounded disk. Our work complements classical works of Ostrovskii, Linnik, Zimogljad and others, as well as recent advances by Michelen and Sahasrabudhe, Eremenko and Fryntov. For applications, our result leads to quantitative central limit theorems applicable to very general and possibly strongly dependent random systems such as discrete spin systems that is based on the theory of Lee-Yang zeros and $alpha$-determinantal processes ($alpha in mathbb{R}$). See Arxiv:2107.08469.

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