Spectral approximation of banded Laurent matrices with localized random perturbations

This paper explores the relationship between the spectra of perturbed infinite banded Laurent matrices L(a)+K and their approximations by perturbed circulant matricesC n (a)+P n KP n for large n. The entries K jk of the perturbation matrices assume values in prescribed sets (omega)jk at the sites (j, k) of a fixed finite set E, and are zero at the sites (j, k) outside E. With K (omega)E denoting the ensemble of these perturbation matrices, it is shown that lim (n-ary union) sp(Cn(a) + PnKPn) = (n-ary union) sp(L(a) + K) under several fairly general assumptions on E and (omega)