  We revisit the problem of computing the boundary density profile of a droplet
of two-dimensional one-component plasma (2D OCP) with logarithmic interaction
between particles in a confining harmonic potential. At a sufficiently low
temperature but still in the liquid phase, the density exhibits oscillations as
a function of the distance to the boundary of the droplet. We obtain the
density profile numerically using Monte-Carlo simulations of the 2D OCP. We
argue that the decay and period of those oscillations can be explained within a
picture of the Wigner crystallization near the boundary, where the crystal is
gradually melted with the increasing distance to the boundary.
