Random matrix products, loop equations and integrability

Applications in random matrix theory of a PIII ′ τ-function sequence from Okamoto's Hamiltonian formulation

D Dai, PJ Forrester, SX Xu

2022-04-01

We consider the singular linear statistic of the Laguerre unitary ensemble (LUE) consisting of the sum of the reciprocal of the ei..

Gromov-Witten invariants of P (1) coupled to a KdV tau function

Paul Norbury

2022-02-22

We consider the pull-back of a natural sequence of cohomology classes Θg,n∈H2(2g−2+n)(M‾g,n,Q) to the moduli space of stable maps ..

Harmonic analysis for rank-1 randomised Horn problems

Jiyuan Zhang, Mario Kieburg, Peter J Forrester

2021-08-01

The randomised Horn problem, in both its additive and multiplicative versions, has recently drawn an increasing interest. Especial..

Linear differential equations for the resolvents of the classical matrix ensembles

Anas A Rahman, Peter J Forrester

2021-07-01

The spectral density for random matrix β ensembles can be written in terms of the average of the absolute value of the characteris..

JNR MONOPOLES

Michael K Murray, Paul Norbury

2021-06-01

We review the theory of JNR, mass 12 hyperbolic monopoles in particular their spectral curves and rational maps. These are used to..

Fox H-kernel and theta-deformation of the Cauchy Two-Matrix Model and Bures Ensemble

Peter J Forrester, Shi-Hao Li

2021-04-01

A $\theta $-deformation of the Laguerre weighted Cauchy two-matrix model, and the Bures ensemble, is introduced. Such a deformatio..

Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap

Peter J Forrester

2021-04-01

We consider properties of the ground state density for the d-dimensional Fermi gas in an harmonic trap. Previous work has shown th..

Classical skew orthogonal polynomials in a two-component log-gas with charges 1 and 2

Peter J Forrester, Shi-Hao Li

2021-03-18

There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue probability d..

Phase Transitions for Products of Characteristic Polynomials under Dyson Brownian Motion

Peter J Forrester, Dang-Zheng Liu

2020-11-04

We study the averaged products of characteristic polynomials for the Gaussian and Laguerre β-ensembles with external source, and p..

Lyapunov Exponents for Some Isotropic Random Matrix Ensembles

PJ Forrester, Jiyuan Zhang

2020-09-01

A random matrix with rows distributed as a function of their length is said to be isotropic. When these distributions are Gaussian..

Parametrising correlation matrices

Peter J Forrester, Jiyuan Zhang

2020-07-01

Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier..

Schwinger-Dyson and loop equations for a product of square Ginibre random matrices

Stephane Dartois, Peter J Forrester

2020-05-01

In this paper, we study the product of two complex Ginibre matrices and the loop equations satisfied by their resolvents (i.e. the..

CLASSICAL DISCRETE SYMPLECTIC ENSEMBLES ON THE LINEAR AND EXPONENTIAL LATTICE: SKEW ORTHOGONAL POLYNOMIALS AND CORRELATION FUNCTIONS

Peter J Forrester, Shi-Hao Li

2020-01-01

The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settin..

A generalisation of the relation between zeros of the complex Kac polynomial and eigenvalues of truncated unitary matrices

Peter J Forrester, Jesper R Ipsen

2019-12-01

The zeros of the random Laurent series 1/μ-∑j=1∞cj/zj, where each cj is an independent standard complex Gaussian, is known to corr..

Recursion scheme for the largest beta-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport

Peter J Forrester, Santosh Kumar

2019-10-18

The largest eigenvalue distribution of the Wishart?Laguerre ensemble, indexed by Dyson parameter and Laguerre parameter a, is fund..

Multiplicative convolution of real asymmetric and real anti-symmetric matrices

Mario Kieburg, Peter J Forrester, Jesper R Ipsen

2019-10-01

The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, ..

Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles

Peter J Forrester, Jesper R Ipsen, Dang-Zheng Liu, Lun Zhang

2019-10-01

In this paper, we highlight the role played by orthogonal and symplectic Harish-Chandra integrals in the study of real-valued matr..

Finite-size corrections at the hard edge for the Laguerre beta ensemble

Peter J Forrester, Allan K Trinh

2019-08-15

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this p..

Meet Andreief, Bordeaux 1886, and Andreev, Kharkov 1882-1883

Peter J Forrester

2019-04-01

The paper "Note sur une relation entre les intégrales définies des produits des fonctions" by C. Andréief is an often cited paper ..

Comment on "Finite size effects in the averaged eigenvalue density ofWigner random-sign real symmetric matrices"

Peter J Forrester, Allan K Trinh

2019-03-15

The recent paper "Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices" by G. S. D..

Topological recursion with hard edges

Leonid Chekhov, Paul Norbury

2019-03-01

We prove a Givental type decomposition for partition functions that arise out of topological recursion applied to spectral curves...

Loop Equations for Gromov-Witten Invariant of P-1

Gaetan Borot, Paul Norbury

2019-01-01

We show that non-stationary Gromov–Witten invariants of P1 can be extracted from open periods of the Eynard–Orantin topological re..

Optimal soft edge scaling variables for the Gaussian and Laguerre even beta ensembles

Peter J Forrester, Allan K Trinh

2019-01-01

The β ensembles are a class of eigenvalue probability densities which generalise the invariant ensembles of classical random matri..

Kac-Rice fixed point analysis for single- and multi-layered complex systems

JR Ipsen, PJ Forrester

2018-11-23

We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian ..

Comment on "Sum of squares of uniform random variables" by I. Weissman

Peter J Forrester

2018-11-01

The recent paper by Weissman (2017) is compared to earlier work of B. Tibken and D. Constales relating to the area of the intersec..

Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra-Itzykson-Zuber Integral

PJ Forrester, JR Ipsen, Dang-Zheng Liu

2018-05-01

We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for..

Selberg integral theory and Muttalib-Borodin ensembles

PJ Forrester, JR Ipsen

2018-04-01

We study Muttalib–Borodin ensembles — particular eigenvalue PDFs on the half-line — with classical weights, i.e. Laguerre, Jacobi ..

Large N expansions for the Laguerre and Jacobi beta-ensembles from the loop equations

Peter J Forrester, Anas A Rahman, Nicholas S Witte

2017-11-01

The β-ensembles of random matrix theory with classical weights have many special properties. One is that the loop equations specif..