{"paper":{"title":"Concentration Inequalities for Sample Cross-Covariances","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Sub-Gaussian sample cross-covariances deviate from their mean in operator norm at a rate governed by the effective ranks of the marginal covariances.","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Daniel Sanz-Alonso, Jiaheng Chen","submitted_at":"2026-05-16T00:58:51Z","abstract_excerpt":"This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed by the effective ranks of the two marginal covariance matrices. 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