An RDT based confirmation of Lehner's formula for Kronecker-Gaussian matrices

Mihailo Stojnic

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arXiv · 2607.26551

An RDT based confirmation of Lehner's formula for Kronecker-Gaussian matrices

Mihailo Stojnic

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Abstract

Remarkable breakthroughs [25,43] established the so-called strong asymptotic freeness between classical Gaussian random ensembles and their semicircular free counterparts. Along the same lines, the Lehner formula [31], associated with the free counterpart, precisely determines the spectral edges of Kronecker-Gaussian matrices. We here revisit and study this formula without the utilization of random matrix theory and spectral methods. In particular, relying on concepts utilized within \emph{Random Duality Theory} (RDT) [45,46,51], we reconfirm Lehner's formula and effectively reprove the key asymptotic freeness results obtained via spectral methods in [25,43].

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Mihailo Stojnic. 2026-07-29. An RDT based confirmation of Lehner's formula for Kronecker-Gaussian matrices. https://arxiv.org/abs/2607.26551

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