Addition to "Structured random matrices and cyclic cumulants: A free probability approach"

TL;DR

This paper refines the definition of structured random matrix ensembles by extending axioms to include cumulants of disjoint cycles, maintaining stability under non-linear transformations.

Contribution

It introduces a refined axiomatic framework for structured random matrices, enhancing the original model to handle more complex cumulant structures.

Findings

The refined axioms extend the class of random matrix ensembles.

Stability under non-linear transformations is preserved.

Theoretical framework now includes cumulants of disjoint cycles.

Abstract

We give a refined definition of the class of random matrix ensembles introduced in our paper "Structured random matrices and cyclic cumulants: A free probability approach" (arXiv:2309.14315) by extending the so-called fourth axiom to deal with cumulants of disjoint cycles. We argue that the theorems concerning the stability of such ensembles under non-linear transformations still hold with these refined axioms.