  Measurements of resonant tunneling through a localized impurity state are
used to probe fluctuations in the local density of states of heavily doped
GaAs. The measured differential conductance is analyzed in terms of correlation
functions with respect to voltage. A qualitative picture based on the scaling
theory of Thouless is developed to relate the observed fluctuations to the
statistics of single particle wavefunctions. In a quantitative theory
correlation functions are calculated. By comparing the experimental and
theoretical correlation functions the effective dimensionality of the emitter
is analyzed and the dependence of the inelastic lifetime on energy is
extracted.
