Abstract: The noncommutative Khintchine inequality is a key tool in analyzing nonhomogeneous random matrices, providing nonasymptotic bounds on the spectral norm of Gaussian random matrices $X = g_1A_1+⋯+g_n A_n$ where $g_i$ are independent Gaussian variables and $A_i$ are matrix coefficients. While it gives sharp logarithmic bounds when $A_i$ commute, it is often suboptimal in noncommutative settings.
In this talk we will introduce the concept of "intrinsic freeness", which provides sharper bounds than the traditional noncommutative Khintchine inequality, especially in cases where the latter is suboptimal. We also show how to use Gaussian interpolation to solve these problems, and finally illustrate the practical significance of this theorem through various examples.

About the Speaker:

论坛每次邀请一位博士生就某个前沿课题做较为系统深入的介绍，主题包括但不限于机器学习、高维统计学、运筹优化和理论计算机科学。