  We study the effect of electron tunneling on the level statistics of quantum
dots. While the coupling between individual levels and the electron reservoir
leads predominantly to the expected level broadening, the indirect coupling of
adjacent levels via the reservoir results in a new asymptotic level statistics
and broadening. These features, which are attributed to renormalized spectral
weights rather than renormalized eigenvalues of the Hamiltonian, are observable
in the asymptotic frequency dependence in an absorption experiment.
