On some properties of the Gauss ensemble of random matrices: Integrable system (Q1110872)

The author considers certain multidimensional integrals arising from the theory of Gaussian ensembles of random matrices. These integrals define the reduced density functions \(F_ N(x_ 1,...,x_ p)\) depending on parameter \(\lambda\). For \(\lambda =1,2,4\) the functions \(F_ N\) have been extensively invetigated. The author takes up the general case. The main result of the paper is the theorem that \(F_ N(x_ 1,..,x_ p)\) satisfy an integrable (in the sense of Frobenius) system of differential equations.