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Complex Approximations, Orthogonal Polynomials and Applications (CAOPA)
17 января 2022 г. 20:00–21:00, г. Москва, online via Zoom at 17:00 GMT (=12:00 EST=18:00 CET=20:00 Msk)
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Supersymmetric approach to the deformed Ginibre ensemble
T. Shcherbina University of Wisconsin-Madison
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Количество просмотров: |
Эта страница: | 162 |
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Аннотация:
We consider non-Hermitian random matrices of the form $H=A+H_0$, where $H_0$ is a standard Ginibre matrix, and $A$ is a rather general $n\times n$ matrix (Hermitian or non-Hermitian) independent of $H_0$. It is known that under some reasonable conditions the limiting spectrum of $H$ lies in some domain $D$ with a smooth boundary $\Gamma$. We apply the supersymmetric approach to study the asymptotic behavior of the smallest singular value of the matrix $(H-z)$ if $z\in D$
but $\mathrm{dist}(z,\Gamma)\sim n^{-1/2}$.
Язык доклада: английский
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