A three-series theorem on Lie groups

TL;DR

This paper extends Kolmogorov's three-series theorem to Lie groups, providing a necessary and sufficient condition for the convergence of independent products, with applications to random matrices.

Contribution

It introduces a three-series theorem for Lie groups, generalizing classical results to a non-abelian setting and applying it to random matrix theory.

Findings

Established a necessary and sufficient condition for convergence of independent products on Lie groups.

Extended classical three-series theorem to the context of Lie groups.

Discussed applications to the convergence of independent random matrices.

Abstract

We obtain a necessary and sufficient condition for the convergence of independent products on Lie groups, as a natural extension of Kolmogorov's three-series theorem. Application to independent random matrices is discussed.