  We study the partition function of a two-dimensional Coulomb gas on a circle,
in the presence of external pointlike charges, in a double scaling limit where
both the external charges and the number of gas particles are large. Our
original motivation comes from studying amplitudes for multi-string emission
from a decaying D-brane in the high energy limit. We analyze the scaling limit
of the partition function and calculate explicit results. We also consider
applications to random matrix theory. The partition functions can be related to
random scattering, or to weights of lattice paths in certain growth models. In
particular, we consider the discrete polynuclear growth model and use our
results to compute the cumulative probability density for the height of long
level-1 paths. We also obtain an estimate for an almost certain maximum height.
