  The classical (i.e. non-quantum) equilibrium statistical mechanics of a
Coulomb fluid living on a pseudosphere (an infinite surface of constant
negative curvature) is considered. The Coulomb fluid occupies a large disk
communicating with a reservoir (grand-canonical ensemble). The total charge $Q$
on the disk fluctuates. In a macroscopic description, the charge correlations
near the boundary circle can be described as correlations of a surface charge
density $\sigma$. In a macroscopic approach, the variance of $Q$ and the
correlation function of $\sigma$ are computed; they are universal. These
macroscopic results are shown to be valid for two solvable microscopic models,
in the limit when the microscopic thickness of the surface charge density goes
to zero.
