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

@article{Park2022OnAC,
  title={On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes},
  author={Jin-woo Park and Huy-Tuan Pham},
  journal={ArXiv},
  year={2022},
  volume={abs/2204.10309}
}
A BSTRACT . For appropriate Gaussian processes, 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, as well as a version of Talagrand’s result for general positive empirical processes. 
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