On the correlation function of the characteristic polynomials of the Hermitian Wigner ensemble

DOI10.1007/s00220-011-1316-8zbMath1232.15028arXiv1006.2536OpenAlexW3098532292MaRDI QIDQ647386

Tatyana Shcherbina

Publication date: 23 November 2011

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.2536

zbMATH Keywords

characteristic polynomialcorrelation functionrandom matrixGaussian Unitary Ensemble

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Hermitian, skew-Hermitian, and related matrices (15B57) Random matrices (algebraic aspects) (15B52)

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Superposition of random plane waves in high spatial dimensions: Random matrix approach to landscape complexity ⋮ On the correlation functions of the characteristic polynomials of the sparse Hermitian random matrices ⋮ Optimal lower bound on the least singular value of the shifted Ginibre ensemble ⋮ Characteristic polynomials for random band matrices near the threshold ⋮ On the Correlation Functions of the Characteristic Polynomials of Random Matrices with Independent Entries: Interpolation Between Complex and Real Cases ⋮ On the correlation functions of the characteristic polynomials of the Hermitian sample covariance matrices ⋮ On the second mixed moment of the characteristic polynomials of 1D band matrices ⋮ Characteristic polynomials for 1D random band matrices from the localization side ⋮ Characteristic polynomials of products of non-Hermitian Wigner matrices: finite-\(N\) results and Lyapunov universality ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ On the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries

Cites Work

• On the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix
• Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach
• Moments of the characteristic polynomial in the three ensembles of random matrices
• Supersymmetry in Disorder and Chaos
• Characteristic polynomials of random matrices.
• Random matrix theory and \(\zeta(1/2+it)\).
• Characteristic polynomials of real symmetric random matrices
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