关于库仑气体的边界约束
On boundary confinements for the Coulomb gas
摘要：
本文引入一类库仑气体系综的边界约束，并在二维随机正规矩阵行列式情形下研究它们。该族在自由边界和硬边缘情况之间进行插值，这些情况已在各种随机矩阵理论中得到了很好的研究。限制也可以放松到自由边界之外，以产生具有更模糊边界的系综，即，在那里粒子越来越有可能在边界之外被发现。由此产生的合奏调查相对于缩放限制和分布的最大模量。特别是，我们证明了存在一个新的点场-一个限制的缩放限制的超弱点时，液滴不再是很好地定义。
英文摘要：
We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with more fuzzy boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field - a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.
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