4 citations · 5 across the 5 of their papers we have counts for
6 papers
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…
Feynman-Kac formula for the stochastic Bessel operator
Patrick Waters
We introduce a stochastic process and functional that should describe the semigroup generated by the stochastic Bessel operator. Recently Gorin and Shkolnikov showed that the large…
Universality of the Stochastic Bessel Operator
Brian Rider, Patrick Waters
We establish universality at the hard edge for general beta ensembles provided that the background potential V is a polynomial such that x -> V(x^2) is uniformly convex and beta is…
Fine structure of moments of the KMK transform of the Poissonized Plancharel measure
Patrick Waters
We consider asymptotics behavior of Poissonized Plancharel measures as the poissonization parameter goes to infinity. Recently Moll proved a convergent series expansion for sta…
Solution of the string equations for asymmetric potentials
Patrick Waters
We consider the large expansion of the partition function for the Hermitian one-matrix model. It is well known that the coefficients of this expansion are generating functions…
Valence independent formula for the equilibrium measure
Patrick Waters
We derive a new formula for the equilibrium measure for eigenvalues of random matrices sampled from polynomial perturbations of the GUE, valid in the one-cut case. The virtue of ou…