Random permutation matrix models for graph products
Ian Charlesworth
Prifysgol Caerdydd, Cardiff, UKRolando de Santiago
California State University, Long Beach, USABen Hayes
University of Virginia, Charlottesville, USADavid Jekel
University of Copenhagen, DenmarkSrivatsav Kunnawalkam Elayavalli
University of California, San Diego, La Jolla, USABrent Nelson
Michigan State University, East Lansing, USA

Abstract
Graph independence (also known as -independence or -independence) is a mixture of classical independence and free independence corresponding to graph products of groups or 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 probabilistic proof that graph products of sofic groups are sofic.
Cite this article
Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson, Random permutation matrix models for graph products. Doc. Math. 30 (2025), no. 5, pp. 1231–1269
DOI 10.4171/DM/992