MAJORIZATION OF GAUSSIAN-PROCESSES AND GEOMETRIC APPLICATIONS

• 成果类型: Article
• 署名作者: GORDON, Y
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01291425
• 发表日期: 1992
• 页码: 251-267
• 关键词: inequality

摘要

Let (x(i)*)i = 1n denote the decreasing rearrangement of a sequence of real numbers (x(i))i = 1n. Then for every i not-equal j, and every 1 less-than-or-equal-to k less-than-or-equal-to n, the 2-nd order partial distributional derivatives satisfy the inequality, partial derivative 2/partial derivative x(i) partial derivative x(j) [GRAPHICS] less-than-or-equal-to 0. As a consequence we generalize the theorem due to Fernique and Sudakov. A generalization of Slepian's lemma is also a consequence of another differential inequality. We also derive a new proof and generalizations to volume estimates of intersecting spheres and balls in R(n) proved by Gromov.