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arXiv · 2609.24023

Infinitesimal Freeness of Wigner Matrices

Samuel Gurrola-Viramontes·James A. Mingo
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Abstract

In this paper, within the framework of real infinitesimal free probability introduced by Cébron and the second author, we compute the real infinitesimal free cumulants of independent complex Wigner matrices. Our approach relies on establishing a combinatorial relation between annular non-crossing partitions and families of directed graphs. As a consequence, we demonstrate that independent complex Wigner matrices are asymptotically real infinitesimally free. In particular, we show (under mild conditions) that a complex Wigner matrix is asymptotically infinitesimally free from its transpose.

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Samuel Gurrola-Viramontes, James A. Mingo. 2026-09-21. Infinitesimal Freeness of Wigner Matrices. https://arxiv.org/abs/2609.24023

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