41 citations · 92 across the 16 of their papers we have counts for
16 papers
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…
Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes
Marco Bertola, Robert Buckingham, Seung-Yeop Lee +1
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the mat…
Spectra of random Hermitian matrices with a small-rank external source: supercritical and subcritical regimes
Marco Bertola, Robert Buckingham, Seung-Yeop Lee +1
Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \c…
Combinatorics of dispersionless integrable systems and universality in random matrix theory
Yuji Kodama, Virgil U. Pierce
It is well-known that the partition function of the unitary ensembles of random matrices is given by a tau-function of the Toda lattice hierarchy and those of the orthogonal and sy…
Duality of real and quaternionic random matrices
Wlodzimierz Bryc, Virgil U. Pierce
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enum…
Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation
Tamara Grava, V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem…