On the concentration of Gaussian Cayley matrices

TL;DR

This paper investigates the concentration properties of Gaussian matrices derived from finite groups' regular representations, proposing them as benchmarks for noncommutative Khintchine inequalities and applying them to the matrix Spencer conjecture.

Contribution

Introduces Gaussian Cayley matrices as a new benchmark for noncommutative Khintchine inequalities and explores their application to the matrix Spencer conjecture.

Findings

Gaussian Cayley matrices exhibit specific concentration behaviors

They serve as effective benchmarks for inequality improvements

Application to the matrix Spencer conjecture demonstrates practical relevance

Abstract

Given a finite group, we study the Gaussian series of the matrices in the image of its left regular representation. We propose such random matrices as a benchmark for improvements to the noncommutative Khintchine inequality, and we highlight an application to the matrix Spencer conjecture.