2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121594We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt random perturbations. We also obtain some results for singular spectral types.Spectral Theorytext