Random matrix theory is now a big subject with applications in many disciplines of science,
engineering and finance. This article is a survey specifically oriented towards the needs and …

We elaborate on a recently conjectured relation of Painlevé transcendents and 2D
conformal field theory. General solutions of Painlevé VI, V and III are expressed in terms of …

We prove a pair of transformations relating elliptic hypergeometric integrals of different
dimensions, corresponding to the root systems BC n and A n; as a special case, we recover …

The six Painlevé equations (PI–PVI) were first discovered around the beginning of the
twentieth century by Painlevé, Gambier and their colleagues in an investigation of nonlinear …

The six Painlevé equations (PI–PVI) were first discovered about a hundred years ago by
Painlevé and his colleagues in an investigation of nonlinear second-order ordinary …

We compute the entropy of entanglement in the ground states of a general class of quantum
spin-chain Hamiltonians—those that are related to quadratic forms of Fermi operators …

Duality identities in random matrix theory for products and powers of characteristic
polynomials, and for moments, are reviewed. The structure of a typical duality identity for the …

The power spectrum is a Fourier series statistic associated with the covariances of the
displacement from average positions of the members of an eigen-sequence. When this …

We study expectations of powers and correlation functions for characteristic polynomials of
non-Hermitian random matrices. For the-point and-point correlation function, we obtain …

The power spectrum analysis of spectral fluctuations in complex wave and quantum systems
has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate …