How Many Eigenvalues of a Product of Truncated Orthogonal Matrices are Real
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In this paper, a truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk.Abstract:
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This ...read more
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Spectral statistics for the difference of two Wishart matrices
Santosh Kumar,S. Sai Charan +1 more
TL;DR: In this article, the authors derived the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches: the first derivation involves the use of unitary group integral and the second one relies on applying the derivative principle.
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Real Eigenvalues of Elliptic Random Matrices
TL;DR: In this article, the real eigenvalues of a real elliptic Ginibre matrix whose entries are correlated through a non-Hermiticity parameter were derived for the almost Hermitian regime.
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On the number of real eigenvalues of a product of truncated orthogonal random matrices
TL;DR: In this paper, it was shown that the real eigenvalues of the product matrix can be approximated by a truncation of the original product matrix, where each matrix in the truncation is an orthogonal matrix.
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Real eigenvalues of elliptic random matrices
TL;DR: In this article, the real eigenvalues of a real elliptic Ginibre matrix whose entries are correlated through a non-Hermiticity parameter were derived for the almost Hermitian regime.
Local central limit theorem for real eigenvalue fluctuations of elliptic GinOE matrices
TL;DR: In this paper , the authors studied the fluctuations of the number of real eigenvalues of Gaussian random matrices from the elliptic Ginibre orthogonal ensemble (GinOE).
References
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Book
Log-Gases and Random Matrices
TL;DR: Forrester as discussed by the authors presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems, and provides hundreds of guided exercises and linked topics.
Journal ArticleDOI
The Probability that a Random Real Gaussian Matrix haskReal Eigenvalues, Related Distributions, and the Circular Law
TL;DR: In this paper, the authors derived the exact expected empirical spectral distribution of the complex eigenvalues for finiten, from which convergence in the expected distribution to the circular law for normally distributed matrices may be derived.
Journal ArticleDOI
Eigenvalue statistics of the real Ginibre ensemble.
Peter J. Forrester,Taro Nagao +1 more
TL;DR: A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented, relevant to May's stability analysis of biological webs.
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Eigenvalue statistics of random real matrices
Nils Lehmann,H. J. Sommers +1 more
TL;DR: The joint probability density of eigenvalues in a Gaussian ensemble of real asymmetric matrices, which is invariant under orthogonal transformations is determined, which indicates thatrices of the type considered appear in models for neural-network dynamics and dissipative quantum dynamics.