45 citations · 137 across the 11 of their papers we have counts for
6 papers · 1 filter
Asymptotic analysis of random matrices with external source and a family of algebraic curves
K. D. T-R McLaughlin
We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with source term containing two distinct eigenvalues. These condit…
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…
Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
A. Martinez-Finkelshtein, K. T. -R. McLaughlin, E. B. Saff
Strong asymptotics of polynomials orthogonal on the unit circle with respect to a weight of the form $$ W(z) = w(z) \prod_{k=1}^m |z-a_k|^{2β_k}, \quad |z|=1, \quad |a_k|=1, \quad…
Asymptotics of Recurrence Relation Coefficients, Hankel Determinant Ratios, and Root Products Associated with Laurent Polynomials Orthogonal with Respect to Varying Exponential Weights
K. T. -R. McLaughlin, A. H. Vartanian, X. Zhou
Orthogonalisation of the (ordered) base with respect to the real inner product $(f,g) \mapsto \int_{\mathbb{R}}f(…
Asymptotics of Laurent Polynomials of Odd Degree Orthogonal with Respect to Varying Exponential Weights
K. T. -R. McLaughlin, A. H. Vartanian, X. Zhou
Let denote the linear space over spanned by , . Define the real inner product (with varying exponential weights) $<\boldsymbo…
Asymptotics of Laurent Polynomials of Even Degree Orthogonal with Respect to Varying Exponential Weights
K. T. -R. McLaughlin, A. H. Vartanian, X. Zhou
Let denote the linear space over spanned by , . Define the real inner product (with varying exponential weights) $\lang…