On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes

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.

• Publication year

  2022

• Venue

  Annals of Mathematics

• Publication date

  2022-04-21

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.48550/arXiv.2204.10309arXiv 2204.10309
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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