Inverse spectral theory for random Jacobi matrices (Q1826216)

For stationary Jacobi matrices the \(w\)-functions are defined and studied. It turns out that these \(w\)-functions are special Herglotz functions. Starting with such a Herglotz function a stationary Jacobi matrix is constructed having it as \(w\)-function, i.e. necessary and sufficient conditions are given for a Herglotz function to be a \(w\)-function of a random stationary Jacobi matrix. The theory is explained selfconsistently and up to some detail.