相关矩阵的Student系综：特征谱和Kullback-Leibler熵
The Student ensemble of correlation matrices: eigenvalue spectrum and Kullback-Leibler entropy
摘要：
我们研究了一个新的合奏的随机相关矩阵有关的多元学生（或更一般的椭圆）随机变量。我们建立了经验相关矩阵的精确态密度，推广了Marcenko-Pastur的结果。尽管我们仍然能够检测到系统偏差，但学生案例中的理论态密度与经验金融数据之间的比较令人惊讶地好。最后，我们计算显式的经验学生矩阵，这是独立的真正的相关矩阵，在高斯的情况下，Kullback-Leibler熵。我们提供这些Kullback-Leibler熵的数值精确值。
英文摘要：
We study a new ensemble of random correlation matrices related to multivariate Student (or more generally elliptic) random variables. We establish the exact density of states of empirical correlation matrices that generalizes the Marcenko-Pastur result. The comparison between the theoretical density of states in the Student case and empirical financial data is surprisingly good, even if we are still able to detect systematic deviations. Finally, we compute explicitely the Kullback-Leibler entropies of empirical Student matrices, which are found to be independent of the true correlation matrix, as in the Gaussian case. We provide numerically exact values for these Kullback-Leibler entropies.
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