Seminar in Random Tensors
Date: March 5, 2021
Time: 11:00AM - 12:00PM
Location: zoom
Speaker: Dan Mikulincer, Weizmann Institute
Title: A central limit theorem for tensor powers
Abstract: We introduce the Wishart tensor as the p'th tensor power of a given random vector X in R^n. This is inspired by the classical Wishart matrix, obtained when p = 2. Sums of independent Wishart tensors appear naturally in several settings, such as empirical moment tensors and random geometric graphs. We will discuss possible connections and recent results. The main focus of the talk will be quantitative estimates for the central limit theorem of Wishart tensors. In this setting, we will explain how Stein's method may be used to exploit the low dimensional structure which is inherent to tensor powers. Specifically, it will be shown that, under appropriate regularity assumptions, a sum of independent Wishart tensors is close to a Gaussian tensor as soon as n^(2p-1)