On the Correlation Functions of the Characteristic Polynomials of Random Matrices with Independent Entries: Interpolation Between Complex and Real Cases

DOI10.15407/mag18.02.159arXiv2201.00219OpenAlexW4293199425MaRDI QIDQ6182184

Ie. Afanasiev

Publication date: 23 January 2024

Published in: Zurnal matematiceskoj fiziki, analiza, geometrii (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.00219

zbMATH Keywords

SUSYrandom matrix theoryGinibre ensemblemoments of characteristic polynomialscorrelation functions of characteristic polynomials

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Cites Work

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• On the correlation functions of the characteristic polynomials of the sparse Hermitian random matrices
• Central limit theorem for linear eigenvalue statistics of elliptic random matrices
• Transfer matrix approach to 1D random band matrices: density of states
• Around the circular law
• Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes
• Characteristic polynomials for 1D random band matrices from the localization side
• Delocalization for a class of random block band matrices
• Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model
• On the correlation function of the characteristic polynomials of the Hermitian Wigner ensemble
• Supersymmetry approach to Wishart correlation matrices: exact results
• Gaussian fluctuations for non-Hermitian random matrix ensembles
• The Ginibre ensemble of real random matrices and its scaling limits
• The probability that a random real Gaussian matrix has \(k\) real eigenvalues, related distributions, and the circular law
• Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach
• Characteristic polynomials of complex random matrix models
• Universality for 1d random band matrices: sigma-model approximation
• On the correlation functions of the characteristic polynomials of the Hermitian sample covariance matrices
• Random matrices: universality of ESDs and the circular law
• Fluctuation around the circular law for random matrices with real entries
• The density of states of 1D random band matrices via a supersymmetric transfer operator
• Supersymmetric polar coordinates with applications to the Lloyd model
• On the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries
• Random matrices: universality of local spectral statistics of non-Hermitian matrices
• Density of states for random band matrices in two dimensions
• Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem
• Superbosonization of invariant random matrix ensembles
• Edge universality for non-Hermitian random matrices
• Optimal lower bound on the least singular value of the shifted Ginibre ensemble
• Averages of characteristic polynomials in random matrix theory
• Universality of level correlation function of sparse random matrices
• Supersymmetry in Disorder and Chaos
• Fluctuation formula for complex random matrices
• An exact formula for general spectral correlation function of random Hermitian matrices
• Random matrices close to Hermitian or unitary: overview of methods and results
• The Strong Circular Law. Twenty years later. Part II
• The Circular Law: ten years later
• Statistical Ensembles of Complex, Quaternion, and Real Matrices
• On the moments of the characteristic polynomial of a Ginibre random matrix
• Density of states for Gaussian unitary ensemble, Gaussian orthogonal ensemble, and interpolating ensembles through supersymmetric approach
• The Noise in the Circular Law and the Gaussian Free Field
• The Strong Circular Law. Twenty years later. Part I
• The Circular Law. Twenty years later. Part III
• On the Correlation Functions of the Characteristic Polynomials of Real Random Matrices with Independent Entries
• Characteristic polynomials of random matrices.
• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation

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