18 citations · 37 across the 13 of their papers we have counts for
5 papers · 1 filter
A Riemann-Hilbert problem for skew-orthogonal polynomials
V. U. Pierce
We find a local Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble…
An algorithm for map enumeration
Virgil U. Pierce
Bauer and Itzykson showed that associated to each labeled map embedded on an oriented Riemann surface there was a group generated by a pair of permutations. From this result an alg…
Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation
V. U. Pierce, Fei-Ran Tian
We study the zero dispersion limit of the fifth order KdV equations when time is sufficiently large. In general, the weak limit may be described by an arbitrary odd number of hyper…
Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations
V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the fifth order KdV equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the solution of the Whi…
Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices
N. M. Ercolani, K. D. T-R McLaughlin, V. U. Pierce
In this paper we derive a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large , of the logarithm of the partitio…