R-transforms for non-Hermitian matrices: a spherical integral approach
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917495135272960 |
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| author | Bousseyroux, Pierre Potters, Marc |
| author_facet | Bousseyroux, Pierre Potters, Marc |
| contents | In this paper, we establish a connection between the formalism of $\mathcal{R}$-transforms for non-Hermitian random matrices and the framework of spherical integrals, using the replica method. This connection was previously proved in the Hermitian setting and in the case of bi-invariant random matrices. We show that the $\mathcal{R}$-transforms used in the non-Hermitian context in fact originate from a single scalar function of two variables. This provides a new and transparent way to compute $\mathcal{R}$-transforms, which until now had been known only in restricted cases such as bi-invariant, Hermitian, or elliptic ensembles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09360 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | R-transforms for non-Hermitian matrices: a spherical integral approach Bousseyroux, Pierre Potters, Marc Disordered Systems and Neural Networks Mathematical Physics Probability In this paper, we establish a connection between the formalism of $\mathcal{R}$-transforms for non-Hermitian random matrices and the framework of spherical integrals, using the replica method. This connection was previously proved in the Hermitian setting and in the case of bi-invariant random matrices. We show that the $\mathcal{R}$-transforms used in the non-Hermitian context in fact originate from a single scalar function of two variables. This provides a new and transparent way to compute $\mathcal{R}$-transforms, which until now had been known only in restricted cases such as bi-invariant, Hermitian, or elliptic ensembles. |
| title | R-transforms for non-Hermitian matrices: a spherical integral approach |
| topic | Disordered Systems and Neural Networks Mathematical Physics Probability |
| url | https://arxiv.org/abs/2601.09360 |