标题： 埃尔米特矩阵模型的总体 universality 和相关性质 显示英文标题

标题： Bulk Universality and Related Properties of Hermitian Matrix Models

摘要： 我们给出了 Hermite 矩阵模型光谱中普遍性性质的一个新证明，假设决定该模型的势是整体上的 $C^{2}$ 函数且局部上是 $C^{3}$ 函数（详见定理 \ref{t:U.t1}）。 我们的证明如同之前在 \cite{Pa-Sh:97} 中的证明一样基于正交多项式技术，但并未使用正交多项式的渐近性质。 相反，我们通过模型相关函数的行列式公式推导出一个特定的非线性积分-微分方程，并将其解作为唯一的 $sin$-核。此外，我们还给出了论文 \cite{BPS:95} 关于特征值限制归一化计数测度的存在性和性质的简化和加强版本。 我们在普遍性的证明中使用了这些结果，并相信它们具有独立的兴趣价值。 显示英文摘要

摘要： We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \ref{t:U.t1}). The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain the $sin$-kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant formulas for the correlation functions of the model. We also give a simplified and strengthened version of paper \cite{BPS:95} on the existence and properties of the limiting Normalized Counting Measure of eigenvalues. We use these results in the proof of universality and we believe that they are of independent interest.