Characteristic polynomials in random matrix theory

A bilateral extension of the q-Selberg integral

Masahiko Ito, Peter J Forrester

2017-04-01

A multi-dimensional bilateral q-series extending the q-Selberg integral is studied using concepts of truncation, regularization an..

The q-Dixon-Anderson integral and multi-dimensional (1)psi(1) summations

Masahiko Ito, Peter J Forrester

2015-03-15

The Dixon-Anderson integral is a multi-dimensional integral evaluation fundamental to the theory of the Selberg integral. The ψ11 ..

Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions

T Can, PJ Forrester, G Tellez, P Wiegmann

2015-03-01

There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann f..

Raney Distributions and Random Matrix Theory

Peter J Forrester, Dang-Zheng Liu

2015-03-01

Recent works have shown that the family of probability distributions with moments given by the Fuss–Catalan numbers permit a simpl..

Loop equation analysis of the circular beta ensembles

NS Witte, PJ Forrester

2015-02-26

Abstract: We construct a hierarchy of loop equations for invariant circular ensembles. These are valid for general classes of pote..

Eigenvalue statistics for product complex Wishart matrices

Peter J Forrester

2014-08-29

The eigenvalue statistics for complex N × N Wishart matrices Xr,s†, Xr,s, where Xr,sis equal to the product of r complex Gaussian ..

Moments of the Gaussian beta ensembles and the large-N expansion of the densities

NS Witte, PJ Forrester

2014-08-01

The loop equation formalism is used to compute the 1/N expansion of the resolvent for the Gaussian β ensemble up to and including ..

Probability of all eigenvalues real for products of standard Gaussian matrices

Peter J Forrester

2014-02-14

With {Xi} independent N × N standard Gaussian random matrices, the probability that all eigenvalues are real for the matrix produc..