A central limit theorem for the determinant of a Wigner matrix

[1]  N. R. Goodman.  The Distribution of the Determinant of a Complex Wishart Distributed Matrix , 1963 .

[2]  A. Prékopa.  ON RANDOM DETERMINANTS I , 1967 .

[3]  B. M. Brown,et al.  Martingale Central Limit Theorems , 1971 .

[4]  V. Alagar.  The distribution of random determinants , 1978 .

[5]  V. Girko.  The Central Limit Theorem for Random Determinants , 1980 .

[6]  G. Szegö,et al.  [52–2] On Certain Hermitian Forms Associated with the Fourier Series of a Positive Function , 1982 .

[7]  H. Trotter.  Eigenvalue distributions of large Hermitian matrices; Wigner's semi-circle law and a theorem of Kac, Murdock, and Szegö , 1984 .

[8]  Vi︠a︡cheslav Leonidovich Girko,et al.  Theory of random determinants , 1990 .

[9]  R. Arratia,et al.  The Cycle Structure of Random Permutations , 1992 .

[10]  Z. Bai,et al.  Convergence rate of expected spectral distributions of large random matrices , 2008 .

[11]  Z. Bai,et al.  Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices , 1993 .

[12]  E. Szemerédi,et al.  On the probability that a random ±1-matrix is singular , 1995 .

[13]  Madan Lal Mehta,et al.  Probability density of the determinant of a random Hermitian matrix , 1998 .

[14]  V. Girko.  A Refinement of the Central Limit Theorem for Random Determinants , 1998 .

[15]  K. Johansson.  On fluctuations of eigenvalues of random Hermitian matrices , 1998 .

[16]  Giovanni M.Cicuta,et al.  Probability density of determinants of random matrices , 2000 .

[17]  Edouard Brézin,et al.  Characteristic Polynomials of Random Matrices , 2000 .

[18]  N. Snaith,et al.  Random Matrix Theory and ζ(1/2+it) , 2000 .

[19]  Delannay,et al.  Distribution of the determinant of a random real-symmetric matrix from the gaussian orthogonal ensemble , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  I. V. Krasovsky.  Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant , 2004 .

[21]  P. J. Forrester,et al.  Applications and generalizations of Fisher–Hartwig asymptotics , 2004 .

[22]  T. Garoni.  On the asymptotics of some large Hankel determinants generated by Fisher–Hartwig symbols defined on the real line , 2004, math-ph/0411019.

[23]  T. Tao,et al.  On the singularity probability of random Bernoulli matrices , 2005, math/0501313.

[24]  G. Rempała,et al.  Asymptotics for products of independent sums with an application to Wishart determinants , 2005 .

[25]  Kevin P. Costello,et al.  Random symmetric matrices are almost surely nonsingular , 2005, math/0505156.

[26]  T. Tao,et al.  On random ±1 matrices: Singularity and determinant , 2006 .

[27]  A. Rouault.  Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles , 2006, math/0607767.

[28]  H. Yau,et al.  Wegner estimate and level repulsion for Wigner random matrices , 2008, 0811.2591.

[29]  T. Tao,et al.  Random matrices: Universality of local eigenvalue statistics , 2009, 0906.0510.

[30]  Horng-Tzer Yau,et al.  Local Semicircle Law and Complete Delocalization for Wigner Random Matrices , 2008, 0803.0542.

[31]  J. W. Silverstein,et al.  Spectral Analysis of Large Dimensional Random Matrices , 2009 .

[32]  Horng-Tzer Yau,et al.  Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices , 2007, 0711.1730.

[33]  Jean Bourgain,et al.  On the singularity probability of discrete random matrices , 2009, 0905.0461.

[34]  H. Yau,et al.  Bulk universality for generalized Wigner matrices , 2010, 1001.3453.

[35]  R. Killip.  Gaussian Fluctuations for β Ensembles , 2010 .

[36]  H. Yau,et al.  Rigidity of eigenvalues of generalized Wigner matrices , 2010, 1007.4652.

[37]  T. Tao,et al.  Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge , 2009, 0908.1982.

[38]  B. Schlein,et al.  A Wegner estimate for Wigner matrices , 2011, 1103.1473.

[39]  Terence Tao,et al.  Random matrices: Universal properties of eigenvectors , 2011, 1103.2801.

[40]  Jun Yin,et al.  Eigenvector distribution of Wigner matrices , 2011, 1102.0057.

[41]  Hoi H. Nguyen,et al.  On the least singular value of random symmetric matrices , 2011, 1102.1476.

[42]  R. Ulrich,et al.  OBSERVING EVOLUTION IN THE SUPERGRANULAR NETWORK LENGTH SCALE DURING PERIODS OF LOW SOLAR ACTIVITY , 2011, 1102.0303.

[43]  T. Tao,et al.  Random covariance matrices: Universality of local statistics of eigenvalues , 2009, 0912.0966.