  We consider planar Coulomb systems consisting of a large number $n$ of
repelling point charges in the low temperature regime, where the inverse
temperature $\beta$ grows at least logarithmically in $n$ as $n \longrightarrow
\infty$, i.e., $\beta\gtrsim \log n$. Under suitable conditions on an external
potential we prove results to the effect that the gas is with high probability
uniformly separated and equidistributed with respect to the corresponding
equilibrium measure (in the given external field). Our results generalize
earlier results about Fekete configurations, i.e., the case $\beta=\infty$.
There are also several auxiliary results which could be of independent
interest. For example, our method of proof of equidistribution (a variant of
"Landau's method") works for general families of configurations which are
uniformly separated and which satisfy certain sampling and interpolation
inequalities.
