  Scanning tunneling miscoscopy is one of the most powerful spectroscopic tools
for single-electron excitations. We show that the conductance fluctuations, or
noise in the conductance, of a tunneling current into an interacting electron
system is dominated by density-density and spin-spin correlations. This allows
one to probe two-particle properties (susceptibilities) and collective
excitations by standard experimental tunneling methods. We demonstrate this
theoretically, using a novel many-body calculation for the multi-center Kondo
problem, including both direct and indirect exchange between magnetic atoms. An
example of the two-particle correlations around a single magnetic adatom in the
Kondo regime, as would be viewed by a scanning tunneling microscope, is given.
The spatial dependance of the charge and spin correlations, including the
formation of the Kondo cloud in the spin sector, are shown.
