  Both the weakly coupled and strong coupling Anderson impurity problems are
characterized by a Fermi-liquid theory with weakly interacting quasiparticles.
In an Anderson box, mesoscopic fluctuations of the effective single particle
properties will be large. We study how the statistical fluctuations at low
temperature in these two problems are connected, using random matrix theory and
the slave boson mean field approximation (SBMFA). First, for a resonant level
model such as results from the SBMFA, we find the joint distribution of energy
levels with and without the resonant level present. Second, if only energy
levels within the Kondo resonance are considered, the distributions of
perturbed levels collapse to universal forms for both orthogonal and unitary
ensembles for all values of the coupling. These universal curves are described
well by a simple Wigner-surmise type toy model. Third, we study the
fluctuations of the mean field parameters in the SBMFA, finding that they are
small. Finally, the change in the intensity of an eigenfunction at an arbitrary
point is studied, such as is relevant in conductance measurements: we find that
the introduction of the strongly-coupled impurity considerably changes the wave
function but that a substantial correlation remains.
