Random permutation matrix models for graph products

  • Ian Charlesworth

    Prifysgol Caerdydd, Cardiff, UK
  • Rolando de Santiago

    California State University, Long Beach, USA
  • Ben Hayes

    University of Virginia, Charlottesville, USA
  • David Jekel

    University of Copenhagen, Denmark
  • Srivatsav Kunnawalkam Elayavalli

    University of California, San Diego, La Jolla, USA
  • Brent Nelson

    Michigan State University, East Lansing, USA
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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