$β$ -Hermite特征值的离散导数渐近性
Discrete Derivative Asymptotics of the $β$-Hermite Eigenvalues
摘要：
本文研究了$β$ -Hermite三对角矩阵与其子矩阵的经验测度之差的渐近性质。我们证明了这种差异有一个确定性的限制和高斯波动。通过测量和连续杨氏图之间的对应关系，确定性极限与Vershik-Kerov-Logan-Shepp曲线。此外，高斯起伏被识别与高斯自由场的截面导数。
英文摘要：
We consider the asymptotics of the difference between the empirical measures of the $β$-Hermite tridiagonal matrix and its minor. We prove that this difference has a deterministic limit and Gaussian fluctuations. Through a correspondence between measures and continual Young diagrams, this deterministic limit is identified with the Vershik-Kerov-Logan-Shepp curve. Moreover, the Gaussian fluctuations are identified with a sectional derivative of the Gaussian free field.
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