Electrostatics of Coulomb gas, lattice paths, and discrete polynuclear growth

Understand

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.