库仑气体的静电学、晶格路径和离散多核生长
Electrostatics of Coulomb gas, lattice paths, and discrete polynuclear growth
摘要：
本文研究了在双标度极限下，在外部点状电荷和气体粒子数都很大的情况下，二维库仑气体在圆上的配分函数.我们最初的动机来自于研究高能量极限下衰变D-膜的多弦辐射的振幅。我们分析了配分函数的标度极限，并计算了显式结果。我们也考虑随机矩阵理论的应用。配分函数可以与随机散射相关，或者与某些生长模型中的晶格路径的权重相关。特别地，我们考虑离散多核增长模型，并使用我们的结果来计算长1级路径的高度的累积概率密度。我们还得到了一个几乎确定的最大高度的估计。
英文摘要：
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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