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Random permutation matrix models for graph products

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arxiv 2404.07350 v2 pith:YBZ4KB6P submitted 2024-04-10 math.OA math.COmath.FAmath.GRmath.PR

classification math.OAmath.COmath.FAmath.GRmath.PR
keywords independencegraphproductsrandomgroupsmatricesmatrixmodels
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abstract

Graph independence (also known as $\epsilon$-independence or $\lambda$-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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universal C$^{\ast}$-Algebras from Graph Products: Structure and Applications

    math.OA 2025-07 conditional novelty 7.0 of 10

    A new family of ambient C*-algebras around graph products yields universal properties, nuclearity/exactness characterizations, a maximal ideal, and new simplicity and trace-uniqueness criteria for graph product C*-algebras.

  2. Khintchine inequalities, trace monoids and Tur\'an-type problems

    math.OA 2025-06 accept novelty 7.0 of 10

    For sums of G-independent semicircle variables, the operator norm is bounded by 2√ω(G) and is exactly the spectral radius of the Cayley graph of the associated trace monoid.

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