Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumeration

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal polynomials. We obtain the first proof of a complete large N expansion for the partition function, for a general class of probability measures on matrices, originally conjectured by Bessis, Itzykson, and Zuber. We prove that the coefficients in the asymptotic expansion are analytic functions of parameters in the original probability measure, and that they are generating functions for the enumeration of labelled maps according to genus and valence. Central to the analysis is a large N expansion for the mean density of eigenvalues, uniformly valid on the entire real axis.Comment: 44 pages, 4 figures. To appear, International Mathematics Research Notice

The price augmented risk premium, theory and application

This note proposes the Price Augmented Risk Premium (PARP), a decomposition of the multivariage risk premium associated with price and income uncertainty. The PARP is used to measure the likely impact on welfare arising from price fluctuations experienced by UK households over the period 1963-97