Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Bousseyroux, Pierre, Potters, Marc
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Fondation du Risque
OpenAlex ID: W7124291631
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