Spectral statistics of non-Hermitian random matrix ensembles

Chen, Ryan C.; Kim, Yujin H.; Lichtman, Jared Duker; Miller, Steven J.; Sweitzer, Shannon; Winsor, Eric

doi:10.1142/s2010326319500059

Cited by 3 publications

(1 citation statement)

References 45 publications

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“…In the GOE/GUE cases, it is a consequence of the well known Wigner's semicircular law. Recently, it has been proved also for the so-called checkerboard matrices, see [4].…”

Section: Numerical Testsmentioning

confidence: 99%

Takagi factorization of matrices depending on parameters and locating degeneracies of singular values

Dieci¹,

Papini²,

Pugliese³

2021

Preprint

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In this work we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the concerns caused by having either a singular value equal to 0 or multiple singular values. For these phenomena, we give theoretical results showing that their codimension is 2, and we further develop and test numerical methods to locate in parameter space values where these occurrences take place. Numerical study of the density of these occurrences is performed.

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“…In the GOE/GUE cases, it is a consequence of the well known Wigner's semicircular law. Recently, it has been proved also for the so-called checkerboard matrices, see [4].…”

Section: Numerical Testsmentioning

confidence: 99%

Takagi factorization of matrices depending on parameters and locating degeneracies of singular values

Dieci¹,

Papini²,

Pugliese³

2021

Preprint

View full text Add to dashboard Cite

show abstract

Takagi Factorization of Matrices Depending on Parameters and Locating Degeneracies of Singular Values

Dieci¹,

Papini²,

Pugliese³

2022

SIAM J. Matrix Anal. Appl.

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Distribution of Eigenvalues of Matrix Ensembles arising from Wigner and Palindromic Toeplitz Blocks

Blackwell¹,

Borade²,

Bose³

et al. 2021

Preprint

Self Cite

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Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of L-functions; this correspondence has allowed RMT to successfully predict many number theoretic behaviors. However there are some operations which to date have no RMT analogue. Our motivation is to find an RMT analogue of Rankin-Selberg convolution, which constructs a new L-functions from an input pair. We report one such attempt; while it does not appear to model convolution, it does create new ensembles with properties hybridizing those of its constituents.For definiteness we concentrate on the ensemble of palindromic real symmetric Toeplitz (PST) matrices and the ensemble of real symmetric matrices, whose limiting spectral measures are the Gaussian and semicircular distributions, respectively; these were chosen as they are the two extreme cases in terms of moment calculations. For a PST matrix A and a real symmetric matrix B, we construct an ensemble of random real symmetric block matrices whose first row is {A, B} and whose second row is {B, A}. By Markov's Method of Moments and the use of free probability, we show this ensemble converges weakly and almost surely to a new, universal distribution with a hybrid of Gaussian and semi-circular behaviors. We extend this construction by considering an iterated concatenation of matrices from an arbitrary pair of random real symmetric sub-ensembles with different limiting spectral measures. We prove that finite iterations converge to new, universal distributions with hybrid behavior, and that infinite iterations converge to the limiting spectral measure of the dominant component matrix.

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Spectral statistics of non-Hermitian random matrix ensembles

Cited by 3 publications

References 45 publications

Takagi factorization of matrices depending on parameters and locating degeneracies of singular values

Takagi factorization of matrices depending on parameters and locating degeneracies of singular values

Takagi Factorization of Matrices Depending on Parameters and Locating Degeneracies of Singular Values

Distribution of Eigenvalues of Matrix Ensembles arising from Wigner and Palindromic Toeplitz Blocks

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