  There is a well known analogy between the Laughlin trial wave function for
the fractional quantum Hall effect, and the Boltzmann factor for the
two-dimensional one-component plasma. The latter requires analytic continuation
beyond the finite geometry used in its derivation. We consider both disk and
cylinder geometry, and focus attention on the exact and asymptotic features of
the edge density. At the special coupling \Gamma := q^2/k_BT=2 the system is
exactly solvable. In particular the k-point correlation can be written as a k
\times k determinant, allowing the edge density to be computed to first order
in \Gamma - 2. A double layer structure is found, which in turn implies an
overshoot of the density as the edge of the leading support is approached from
inside the plasma. Asymptotic analysis shows that the deviation from the
leading order (step function) value is different for into the plasma than for
outside. For general \Gamma, a Gaussian fluctuation formula is used to study
the large deviation form of the density for N large but finite. This asymptotic
form involves thermodynamic quantities which we independently study, and
moreover an appropriate scaling gives the asymptotic decay of the limiting edge
density outside of the plasma.
