32 citations · 140 across the 26 of their papers we have counts for
10 papers · 1 filter
Yang-Mills-Higgs Equations on Spherical Orbifolds
Nicholas M. Ercolani
In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connec…
Map enumeration from a dynamical perspective
Nicholas Ercolani, Joceline Lega, Brandon Tippings
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlevé equations) and asymptotic analysis of orthogonal poly…
Multiple Scale Asymptotics of Map Enumeration
Nicholas Ercolani, Joceline Lega, Brandon Tippings
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar…
Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel-Appell polynomials
Nicholas M. Ercolani, Patrick Waters
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions assoc…
Conservation Laws of Random Matrix Theory
Nicholas M. Ercolani
This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponenti…
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
Nicholas M. Ercolani, Virgil U. Pierce
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. I…