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

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

2010-03-18

arxiv.org/abs/1003.3663v2

J.Phys.A43:425006,2010

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 8 figures. v2: Text reorganized, references and acknowledgments added, figure 7 modified

Scientific paper

10.1088/1751-8113/43/42/425006

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.

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