Appendix to "Real second-order freeness and the asymptotic real second-order freeness of several real matrix models": Examples and Diagrams

TL;DR

This paper provides illustrative examples and diagrams that visualize the proofs of real second-order freeness in matrix models, connecting matrix calculations with topological surface gluings and permutations.

Contribution

It introduces a visual and topological approach to understanding proofs of real second-order freeness in matrix models, complementing the main paper.

Findings

Matrix calculations can be represented by topological surface gluings.

Surface gluings can be encoded as permutations.

Visual diagrams aid in understanding complex proofs.

Abstract

We present examples and diagrams illustrating the proofs appearing in "Real second-order freeness and the asymptotic real second-order freeness of several real matrix models", to which this paper is meant to be an appendix. We show how matrix calculations may be represented by topological surface gluings, which may in turn be represented as permutations.