Isospectral deformations of random Jacobi operators (Q1208032)

Defining a dynamical system as an automorphism of the probability space, the author establishes the integrability of infinite dimensional Hamiltonian systems obtained by making isospectral deformations of random Jacobi operators. The author shows also that time 1 map of such a so- called random Toda flow can be expressed by a \(QR\) decomposition (that is, as a product of two matrices \(Q\) and \(R\) where \(Q\) is orthogonal and \(R\) is upper triangular). A number of questions are raised which fellow research workers will find interesting.