Addition to "Structured random matrices and cyclic cumulants: A free probability approach"

2025/05/27 by Denis Bernard, Bernard, Denis, Ludwig Hruza +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2505.21376

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a refined definition of the class of random matrix ensembles introduced in our paper "Structured random matrices and cyclic cumulants: A free probability approach" (arXiv:2309.14315) by extending the so-called fourth axiom to deal with cumulants of disjoint cycles. We argue that the theorems concerning the stability of such ensembles under non-linear transformations still hold with these refined axioms.

Citations

• Entrywise application of non-linear functions on orthogonally invariant matrices
• Structured random matrices and cyclic cumulants: A free probability approach
• On a Method of Calculation of Semi-Invariants

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