Recently, Dial et al. presented measurements of the tunneling density of
states into the bulk of a two dimensional electron gas under strong magnetic
fields. Several high energy features appear in the measured spectrum showing a
distinct dependence on filling factor and a unique response to temperature. We
present a quantitative account of the observed structure, and argue it results
from the repulsive Coulomb interactions between the tunneling electron and
states localized at disorder potential wells. The quenching of the kinetic
energy by the applied magnetic field leads to an electron addition spectrum
that is primarily determined by the external magnetic field and is nearly
independent of the disorder potential. Using a Hartree-Fock model we reproduce
the salient features of the observed structure
