Random permutation matrix models for graph products

Ian Charlesworth; Rolando de Santiago; Ben Hayes; David Jekel; Srivatsav Kunnawalkam Elayavalli; Brent Nelson

doi:10.4171/dm/992

JournalsdmVol. 30, No. 5pp. 1231–1269

Random permutation matrix models for graph products

Ian Charlesworth
Prifysgol Caerdydd, Cardiff, UK
- MathSciNet
- ORCID
Rolando de Santiago
California State University, Long Beach, USA
- MathSciNet
- ORCID
Ben Hayes
University of Virginia, Charlottesville, USA
David Jekel
University of Copenhagen, Denmark
Srivatsav Kunnawalkam Elayavalli
University of California, San Diego, La Jolla, USA
- MathSciNet
- ORCID
Brent Nelson
Michigan State University, East Lansing, USA
- MathSciNet
- ORCID

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Abstract

Graph independence (also known as $ε$ -independence or $Λ$ -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