  We substantially extend our relaxation theory for perturbed many-body quantum
systems from [Phys. Rev. Lett. 124, 120602 (2020)] by establishing an
analytical prediction for the time-dependent observable expectation values
which depends on only two characteristic parameters of the perturbation
operator: its overall strength and its range or band width. Compared to the
previous theory, a significantly larger range of perturbation strengths is
covered. The results are obtained within a typicality framework by solving the
pertinent random matrix problem exactly for a certain class of banded
perturbations and by demonstrating the (approximative) universality of these
solutions, which allows us to adopt them to considerably more general classes
of perturbations. We also verify the prediction by comparison with several
numerical examples.
