ar X iv : 0 80 1 . 18 58 v 1 [ m at h - ph ] 1 1 Ja n 20 08 LECTURES ON RANDOM MATRIX MODELS . THE RIEMANN - HILBERT APPROACH

ar X iv : m at h - ph / 0 50 90 44 v 2 1 1 Ja n 20 06 RANDOM POLYNOMIALS , RANDOM MATRICES AND L - FUNCTIONS

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.

ar X iv : m at h - ph / 0 20 10 24 v 1 1 0 Ja n 20 02 Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g + 1 disjoint intervals, J := ∪ g+1 j=1 (a j , b j), with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.

ar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION

ar X iv : 0 80 1 . 35 64 v 1 [ as tr o - ph ] 2 3 Ja n 20 08 Local Phase Space - Shaped by Chaos ?

ar X iv : 0 80 1 . 25 00 v 1 [ co nd - m at . o th er ] 1 6 Ja n 20 08 Making , probing and understanding ultracold Fermi