{"ID":2827152,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.17674","arxiv_id":"2512.17674","title":"On the supremum and its location of the standardized uniform empirical process","abstract":"We show that the maximizing point and the supremum of the standardized uniform empirical process converge in distribution. Here, the limit variable (Z, Y ) has independent components. Moreover, Z attains the values zero and one with equal probability one half and Y follows the Gumbel-distribution.","short_abstract":"We show that the maximizing point and the supremum of the standardized uniform empirical process converge in distribution. Here, the limit variable (Z, Y ) has independent components. Moreover, Z attains the values zero and one with equal probability one half and Y follows the Gumbel-distribution.","url_abs":"https://arxiv.org/abs/2512.17674","url_pdf":"https://arxiv.org/pdf/2512.17674v1","authors":"[\"Dietmar Ferger\"]","published":"2025-12-19T15:16:09Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}