The non-Hermitian minor process
Giorgio Cipolloni, L\'aszl\'o Erd\H{o}s, Oleksii Kolupaiev
TL;DR
This paper demonstrates that the log-determinants of principal minors of large non-Hermitian matrices converge to a 2+1D Gaussian field with logarithmic correlations, revealing a universality class similar to Edwards-Wilkinson.
Contribution
It introduces a new universality result connecting non-Hermitian matrix minors to a specific Gaussian field with logarithmic correlations.
Findings
Log-determinants converge to a 2+1D Gaussian field.
The Gaussian field exhibits logarithmic correlations.
Resembles Edwards-Wilkinson universality class.
Abstract
We show that the log-determinant of leading principal minors of large non-Hermitian random matrices converges in distribution to a 2+1 dimensional Gaussian field, which is logarithmically correlated for the parabolic distance, reminiscent to the Edwards-Wilkinson universality class.
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