  The universal eigenvalue distribution characterizing the Gram matrix of
semiclassical ensembles of black hole microstates is recognized as the
Marchenko-Pastur distribution, which plays a prominent role as the universal
limit distribution in a large class of random matrix and vector models. It is
proposed that this distribution also universally determines the energy spectral
density of black holes, which allows to construct a Krylov space for the time
evolution of typical black hole states and calculate their state complexity. It
is checked that the state complexity growth at late times saturates Lloyd's
bound. Some implications of the proposed spectral density for the generation of
Hawking radiation and black hole evaporation are discussed.
