We introduce and study stochastic \(N\)-particle ensembles which are discretizations for general-\(\beta \) log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, \((z,w)\)-measures, etc. We prove that under technical assumptions on general analytic potential, the global fluctuations for such ensembles are asymptotically Gaussian as \(N\to \infty \). The covariance is universal and coincides with its counterpart in random matrix theory.

中文翻译：

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离散\（\ beta \）-集合的高斯渐近性

我们介绍和研究随机\（N \）粒子集合，它们是随机矩阵理论的一般\（\ beta \）对数气体的离散化。这些示例包括随机平铺，非相交路径族，\（（z，w）\）-测度等。我们证明，在关于一般分析潜能的技术假设下，此类合奏的整体涨落是渐近高斯的，例如\（ N \\ infty \）。协方差是通用的，并且与随机矩阵理论中的对应方一致。