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Numerical ranges of non-normal random matrices: elliptic Ginibre and non-Hermitian Wishart ensembles
Sung-Soo Byun, Joo Young Park
The numerical range of a non-normal matrix plays a central role as a descriptor of non-normal effects beyond spectral information. We study a class of fundamental non-Hermitian ran…
Upper tail large deviations for extremal eigenvalues of the real, complex and symplectic elliptic Ginibre matrices
Sung-Soo Byun, Yong-Woo Lee, Seungjoon Oh
We consider the elliptic Ginibre ensembles in the real, complex and symplectic symmetry classes. As the matrix size tends to infinity, we derive the asymptotic behaviour of the upp…
-deformation of the Marchenko-Pastur law
Sung-Soo Byun, Yeong-Gwang Jung, Guido Mazzuca
We study a -deformed random unitary ensemble associated with the little- Laguerre weight, which provides a discrete analogue of the classical Laguerre unitary ensemble. In th…
-deformed Gaussian unitary ensemble: spectral moments and genus-type expansions
Sung-Soo Byun, Peter J. Forrester, Jaeseong Oh
The eigenvalue probability density function of the Gaussian unitary ensemble permits a -extension related to the discrete -Hermite weight and corresponding -orthogonal pol…
Harer-Zagier type recursion formula for the elliptic GinOE
Sung-Soo Byun
We consider the real eigenvalues of the elliptic Ginibre matrix indexed by the non-Hermiticity parameter , and present a Harer-Zagier type recursion formula for the eve…