On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
成果类型：
Article
署名作者：
Park, Jinyoung; Pham, Huy tuan
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2024.199.3.6
发表日期：
2024
页码：
1293-1321
关键词：
摘要：
For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-p setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.