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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 ϵ\epsilon-independence or λ\lambda-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.

Keywords

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

R2 v1 2026-06-28T15:50:31.131Z