  Current-correlations are a very sensitive probe of the fluctuations of small
conductors. For non-interacting particles injected from thermal sources there
is a simple connection between the sign of correlations and statistics:
current-current correlations of Fermions are negative, intensity-intensity
correlations of Bosons can be positive. In contrast to photons, electrons are
interacting entities, and we can expect the simple connection between
statistics and the sign of current-current correlations to be broken, if
interactions play a crucial role. We present a number of examples in which
interactions are important. At a voltage probe the potential fluctuates to
maintain zero current. It is shown that there are geometries for which these
fluctuations lead to positive correlations. Displacement currents at
capacitively coupled contacts are also positively correlated if both contacts
contribute to screening of the same excess charge fluctuation. Hybrid normal
superconducting systems provide another example which permits positive
correlations. The conditions for positive correlations differ strongly
depending on whether the normal conductor is open and well coupled to the
superconductor or is only weakly coupled via a barrier to the superconductor.
In latter case, positive correlations result if the partition noise generated
by Cooper pairs is overcome by pairs which are broken up and emit one electron
into the contacts of interest.
