We study the effect of electron tunneling on the level statistics of q
uantum dots. While the coupling between individual levels and the elec
tron reservoir leads predominantly to the expected level broadening, t
he indirect coupling of adjacent levels via the reservoir results in n
ew asymptotic level statistics and broadening. These features, which a
re attributed to renormalized spectral weights rather than to renormal
ized eigenvalues of the Hamiltonian, are observable in the asymptotic
frequency dependence in an absorption experiment. [S0031-9007(98)07630
-3].