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

Jinyoung Park; Huy Tuan Pham

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arXiv · 2204.10309

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

Jinyoung Park·Huy Tuan Pham

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Abstract

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.

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Jinyoung Park, Huy Tuan Pham. 2022-04-21. On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes. https://arxiv.org/abs/2204.10309

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