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Eigenvector overlaps of sample covariance matrices with intersecting time periods

Volodymyr Riabov, Konstantin Tikhonov and Jean-Philippe Bouchaud

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Abstract: We compute exactly the overlap between the eigenvectors of two large empirical covariance matrices computed over intersecting time intervals, generalizing the results obtained previously for non-intersecting intervals. Our method relies on a particular form of Girko linearisation and extended local laws. We check our results numerically and apply them to financial data.

Date: 2025-09
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