{"ID":2828042,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.15427","arxiv_id":"2512.15427","title":"Statistics of Min-max Normalized Eigenvalues in Random Matrices","abstract":"Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus, this study investigates the statistical properties of min-max normalized eigenvalues in random matrices. Previously, the effective distribution for such normalized eigenvalues has been proposed. In this study, we apply it to evaluate a scaling law of the cumulative distribution. Furthermore, we derive the residual error that arises during matrix factorization of random matrices. We conducted numerical experiments to verify these theoretical predictions.","short_abstract":"Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus, this study investigates the statistical properties of min-max normalized eigenval...","url_abs":"https://arxiv.org/abs/2512.15427","url_pdf":"https://arxiv.org/pdf/2512.15427v1","authors":"[\"Hyakka Nakada\",\"Shu Tanaka\"]","published":"2025-12-17T13:19:32Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cond-mat.stat-mech\",\"math.ST\"]","methods":"[]","has_code":false}