TL;DR
This paper computes the large N limit of the mean spectral density for sub-unitary matrices using a saddle point method, confirming results from free probability theory.
Contribution
It introduces a modified saddle point approach to derive the asymptotic spectral density of sub-unitary ensembles, aligning with free probability results.
Findings
Large N spectral density matches free probability predictions
Modified saddle point method effectively computes asymptotic densities
Results unify matrix ensemble analysis with free probability theory
Abstract
The large N limit of mean spectral density for the ensemble of NxN sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41 (2008) 50201) is calculated by a modification of the saddle point method. It is shown that the result coincides with the one obtained within the free probability theory by Haagerup and Larsen (J. Funct. Anal. 176 (2000) 331).
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