We study matrix models involving Pfaﬃan interactions as generalizations of the standard β = 1 and β = 4 matrix models. We present the Pfaﬃan formulas for the partition function and the characteristic polynomial averages. We also explore the matrix chain with the Pfaﬃan interaction, which realizes the BCD -type quiver matrix models.

We introduce a new class of two(multi)-matrix models of positive Hermitian matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more… Expand

The general correlation function for the eigenvalues of p complex Hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.

We compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for… Expand

Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments,… Expand

We prove Drinfeld's conjecture that the center of a certain completion of the universal enveloping algebra of an affine Kac-Moody algebra at the critical level is isomorphic to the Gelfand-Dikii… Expand