论文标题
具有径向对称电势的确定性和PFAFFIAN库仑气体的分区功能
Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials
论文作者
论文摘要
我们考虑随机的正常矩阵和平面符号合并，可以将其解释为具有决定性和PFAFFIAF型结构的二维库仑气体。对于一般的径向对称势，我们得出了日志分区函数的渐近扩展，直到$ o（1）$ - 术语随着粒子的数量$ n $的增加而增加。值得注意的是，我们的发现强调，在这些扩展中，$ O（\ log n）$ - 和$ o（1）$的公式取决于液滴的连接性。对于随机的正常矩阵集合，我们的公式与Zabrodin和Wiegmann提出的预测达到了通用添加剂常数。对于平面符号合奏，这些扩展包含$ O（n）$ - 项中的一种新型成分，除了合奏的熵外，还在原点上评估的对数电位。
We consider random normal matrix and planar symplectic ensembles, which can be interpreted as two-dimensional Coulomb gases having determinantal and Pfaffian structures, respectively. For general radially symmetric potentials, we derive the asymptotic expansions of the log-partition functions up to and including the $O(1)$-terms as the number $N$ of particles increases. Notably, our findings stress that the formulas of the $O(\log N)$- and $O(1)$-terms in these expansions depend on the connectivity of the droplet. For random normal matrix ensembles, our formulas agree with the predictions proposed by Zabrodin and Wiegmann up to a universal additive constant. For planar symplectic ensembles, the expansions contain a new kind of ingredient in the $O(N)$-terms, the logarithmic potential evaluated at the origin in addition to the entropy of the ensembles.
