标题： 随机正规矩阵与多项式曲线 显示英文标题

标题： Random Normal Matrices and Polynomial Curves

摘要： 我们证明，在大矩阵极限下，谱位于紧致区域内部且具有特殊类势的正规矩阵模型的特征值均匀填充一个多项式曲线的内部，该曲线由其内部区域的面积及其外部调和矩量唯一定义，这些量均作为势的参数给出。 然后我们考虑与该矩阵模型对应的正交多项式，并证明，在某些假设下，大矩阵极限下单个最高相关正交多项式的零点密度（乘以某个常数因子后）由该多项式曲线的施瓦茨函数的间断性给出。 显示英文摘要

摘要： We show that in the large matrix limit, the eigenvalues of the normal matrix model for matrices with spectrum inside a compact domain with a special class of potentials homogeneously fill the interior of a polynomial curve uniquely defined by the area of its interior domain and its exterior harmonic moments which are all given as parameters of the potential. Then we consider the orthogonal polynomials corresponding to this matrix model and show that, under certain assumptions, the density of the zeros of the highest relevant orthogonal polynomial in the large matrix limit is (up to some constant factor) given by the discontinuity of the Schwarz function of this polynomial curve.