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Random matrices: The Four Moment Theorem for Wigner ensembles
Terence Tao, Van Vu
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Mome…
A central limit theorem for the determinant of a Wigner matrix
Terence Tao, Van Vu
We establish a central limit theorem for the log-determinant of a Wigner matrix , under the assumption of four matching moments with either the GUE or GOE en…
Random matrices: Universal properties of eigenvectors
Terence Tao, Van Vu
The four moment theorem asserts, roughly speaking, that the joint distribution of a small number of eigenvalues of a Wigner random matrix (when measured at the scale of the mean ei…
The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
Terence Tao, Van Vu
A well known conjecture of Wigner, Dyson, and Mehta asserts that the (appropriately normalized) -point correlation functions of the eigenvalues of random Wigner mat…