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On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
Jinyoung Park, Huy Tuan Pham · 2022-04-22 · via math.PR updates on arXiv.org

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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