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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{gurrolaviramontes2026infinitesimal,
  title = {{Infinitesimal Freeness of Wigner Matrices}},
  author = {Samuel Gurrola-Viramontes and James A. Mingo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24023},
  eprint = {2609.24023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24023},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Infinitesimal Freeness of Wigner Matrices
AU  - Samuel Gurrola-Viramontes
AU  - James A. Mingo
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24023
UR  - https://arxiv.org/abs/2609.24023
AB  - 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.
ER  -