Title :Gaussian fluctuations for spin systems and point processes: Near-optimal rates via quantitative Marcinkiewicz’s theorem.

Abstract: 

In this talk, He would like to introduce a broad, quantitative extension of the classical Marcinkiewicz’s theorem to establish central limit theorems (CLTs) with explicit rates of convergence. In particular, we obtain quantitative decay estimates on the Kolmogorov-Smirnov distance between a random variable X and a Gaussian under the condition that the characteristic function Ψ does not vanish only on a bounded disk. This leads to quantitative CLTs applicable to very general and possibly strongly dependent random systems with a near-optimal rate of convergence. Later, He will apply this method for two important classes of models in probability and statistical physics, namely, spin systems and α-determinantal processes. These applications demonstrate the significance of having to control the characteristic function only on a (small) disk, and lead to CLTs which, to the best of our knowledge, are not known in generality. This is a joint work with T.-C. Dinh and S. Ghosh.

About the Speaker:

Hoang Son Tran (Tran Hoang Son in Vietnamese) is doing PhD in Mathematics at National University of Singapore, under the supervision of Prof Subhroshekhar Ghosh and Prof. Tien Cuong Dinh. His research interests are Probability Theory, Mathematical Physics, Complex Analysis and Complex Dynamics. He loves playing football in his free time. He enjoys walking for sightseeing and learning about the culture of Asian countries. This is his second visit to India and he enjoys Indian food.