Eigenvalue correlations on Hyperelliptic Riemann surfaces

Abstract

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, $J:={\cup }_{j=1}^{g+1}(a_j,b_j),$ 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.

latex 2e, seven pages, one figure. To appear in Journal of Physics A

Cited by in corpus (3)

• Double Scaling Limit in Random Matrix Models and a Nonlinear Hierarchy of Differential Equations
• Painlevé V, Painlevé XXXIV and the Degenerate Laguerre Unitary Ensemble
• On tau functions for orthogonal polynomials and matrix models