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The classical (i.e. non-quantum) equilibrium statistical mechanics of aCoulomb fluid living on a pseudosphere (an infinite surface of constantnegative curvature) is considered. The Coulomb fluid occupies a large diskcommunicating with a reservoir (grand-canonical ensemble). The total charge $Q$on the disk fluctuates. In a macroscopic description, the charge correlationsnear the boundary circle can be described as correlations of a surface chargedensity $\sigma$. In a macroscopic approach, the variance of $Q$ and thecorrelation function of $\sigma$ are computed; they are universal. Thesemacroscopic results are shown to be valid for two solvable microscopic models,in the limit when the microscopic thickness of the surface charge density goesto zero.Comment: 19 pages, LaTe

Charge Fluctuations for a Coulomb Fluid in a Disk on a Pseudosphere