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Spectral statistics of the uni-modular ensemble. (English) Zbl 1407.60009

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
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[1] Anderson G W, Guionnet A and Zeitouni O 2009 An Introduction to Random Matrices(Cambridge Studies in Advanced Mathematics vol 118) (Cambridge: Cambridge University Press)
[2] Wigner E P 1955 Characteristic vectors of bordered matrices with infinite dimensions Ann. Math.62 548-64
[3] Wigner E P 1958 On the distribution of the roots of certain symmetric matrices Ann. Math.67 325-8
[4] Sodin S 2007 Random matrices, nonbacktracking walks, and orthogonal polynomials J. Math. Phys.48 123503
[5] Feldheim O N and Sodin S 2010 A universality result for the smallest eigenvalues of certain sample covariance matrices Geom. Funct. Anal.20 88-123
[6] Sodin S 2016 Fluctuations of interlacing sequences J Math. Phys. Anal. Geom. (arxiv:1610.02690) in press
[7] Lakshminarayan A, Puchala Z and Zyczkowski K 2014 Diagonal unitary entangling gates and contradiagonal quantum states Phys. Rev. A 90 032303
[8] Dyson F J 1962 A Brownian motion model for the eigenvalues of a random matrix J. Math. Phys.3 1191-8
[9] Meckes E 2009 On Stein’s Method for Multivariate Normal Approximation(Collections vol 5) (Beachwood, OH: Institute of Mathematical Statistics) pp 153-78
[10] Harer J and Zagier D 1986 The Euler characteristic of the moduli space of curves Invent. Math.85 457-85
[11] Ledoux M 2009 A recursion formula for the moments of the gaussian orthogonal ensemble Ann. Inst. Henri Poincare45 754-69
[12] Witte N S and Forrester P J 2014 Moments of the Gaussian β-ensembles and the large-N expansion of the densities J. Math. Phys.55 083302
[13] Mezzadri F, Reynolds A and Winn B 2017 Moments of the eigenvalue densities and of the secular coefficients of β-ensembles Nonlinearity30 1034
[14] Mezzadri F and Simm N J 2011 Moments of the transmission eigenvalues, proper delay times and random matrix theory I and II J. Math. Phys.52 103511
[15] Mezzadri F and Simm N J 2012 Moments of the transmission eigenvalues, proper delay times and random matrix theory I and II J. Math. Phys.53 053504
[16] Mezzadri F and Simm N J 2013 Tau-function theory of Chaotic quantum transport with β = 1, 2, 4 Commun. Math. Phys.324 465-513
[17] Cunden F, Mezzadri F, Simm N and Vivo P 2016 Large-N expansion for the time-delay matrix of ballistic chaotic cavities J. Math. Phys.57 111901
[18] Girko V L 1989 Asymptotics of the distribution of the spectrum of random matrices Russian Mathematical Surveys vol 44 (London: Turpion) pp 3-36
[19] Pastur L A and Shcherbina M 2011 Eigenvalue Distribution of Large Random Matrices vol 171 (Providence, RI: American Mathematical Society)
[20] Jonsson D 1982 Some limit theorems for the eigenvalues of a sample covariance matrix J. Multivariate Anal.12 1-38
[21] Johansson K 1998 On fluctuations of eigenvalues of random Hermitian matrices Duke Math. J.91 151-204
[22] Khorunzhy A M, Khoruzhenko B A and Pastur L A 1996 Asymptotic properties of large random matrices with independent entries J. Math. Phys.37 5033-60
[23] Sinai Y and Soshnikov A 1998 Central limit theorem for traces of large random matrices with independent matrix elements Bull. Braz. Math. Soc.29 1-24
[24] Chatterjee S 2007 Fluctuations of eigenvalues and second order Poincaré inequalities Probab. Theory Relat. Fields143 1-40
[25] Cabanal-Duvillard T 2001 Fluctuations de la loi empirique deagrandes matrices aléatoires Ann. Inst. Henri Poincare B 37 373-402
[26] Pastur L A 1972 On the spectrum of random matrices Theor. Math. Phys.10 102-12
[27] Efetov K B 1983 Supersymmetry and theory of disordered metals Adv. Phys.32 53
[28] Verbaarschot J J M, Weidenm H A and Zirnbauer M R 1985 Grassmann integration in stochastic quantum physics: the case of compound-nucleus scattering Phys. Rep.129.6 367-438
[29] Pluhar Z and Weidenmüller H A 2015 Quantum graphs and random-matrix theory J. Phys. A: Math. Theor.48 275102
[30] Zirnbauer M R 1996 Supersymmetry for systems with unitary disorder: circular ensembles J. Phys. A: Math. Gen.29 7113
[31] Gnutzmann S and Altland A 2004 Universal spectral statistics in quantum graphs Phys. Rev. Lett.93 194101
[32] Gnutzmann S and Altland A 2005 Spectral correlations of individual quantum graphs Phys. Rev. E 72 056215
[33] Kalisch F and Braak D 2002 Exact density of states for finite Gaussian random matrix ensembles via supersymmetry J. Phys. A: Math. Gen.35 9957
[34] Shamis M 2013 Density of states for Gaussian unitary ensemble, Gaussian orthogonal ensemble and interpolating ensembles through supersymmetric approach J. Math. Phys.54 113505
[35] Mehta M L 2004 Random Matrices vol 142 (New York: Academic)
[36] Oren I, Godel A and Smilansky U 2009 Trace formulae and spectral statistics for discrete Laplacians on regular graphs (I) J. Phys. A: Math. Theor.42 415101
[37] Oren I and Smilansky U 2010 Trace formulae and spectral statistics for discrete Laplacians on regular graphs (II) J. Phys. A: Math. Theor.43 225205
[38] Maciążek T, Joyner C H and Smilansky U 2015 The probability distribution of spectral moments for the Gaussian β-ensembles Acta Phys. Pol. A 128 12
[39] Sosoe P and Wong P 2013 Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices Adv. Math.249 37-87
[40] Joyner C H and Smilansky U 2015 Spectral statistics of Bernoulli matrix ensembles-a random walk approach (I) J. Phys. A: Math. Theor.48 255101
[41] Stein C 1972 A bound for the error in the normal approximation to the distribution of a sum of dependent random variables Proceedings of the 6th Berkeley Symp. on Mathematical Statistics and Probability(Probability Theory vol 2) (Berkeley, CA: University of California Press) pp 583-602
[42] Kusalik T, Mingo J and Speicher R 2007 Orthogonal polynomials and fluctuations of random matrices J. Reine Angew. Math.604 1-46
[43] Schenker J and Schulz-Baldes H 2007 Gaussian fluctuations for random matrices with correlated entries Int. Math. Res. Not.15 rnm047
[44] Risken H 1989 The Fokker-Planck Equation Methods of Solution and Applications(Springer Series in Synergetics vol 18) 2nd edn (Berlin: Springer)
[45] Gardiner C 2009 Stochastic methods A Handbook for the Natural and Social Sciences(Springer Series in Synergetics) 4th edn (Berlin: Springer)
[46] Döbler C and Stolz M 2011 Stein’s method and the multivariate CLT for traces of powers on the compact classical groups Electron. J. Probab.16 2375-405
[47] Webb C 2015 Linear statistics of the circular β-ensemble, Stein’s method and circular Dyson Brownian motion (arxiv:1507.08670)
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