Random permutation matrix models for graph products
Operator Algebras
2024-09-27 v2 Combinatorics
Functional Analysis
Group Theory
Probability
Abstract
Graph independence (also known as -independence or -independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain random permutation matrices, we construct random matrix models for graph independence with amalgamation over the diagonal matrices. This yields a new probabilist,ic proof that graph products of sofic groups are sofic.
Cite
@article{arxiv.2404.07350,
title = {Random permutation matrix models for graph products},
author = {Ian Charlesworth and Rolando de Santiago and Ben Hayes and David Jekel and Brent Nelson and Srivatsav Kunnawalkam Elayavalli},
journal= {arXiv preprint arXiv:2404.07350},
year = {2024}
}
Comments
29 pages, multiple figures. Minor replacements, correcting typos etc. arXiv admin note: substantial text overlap with arXiv:2305.19463