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.


Jinyoung Park

Courant Institute of Mathematical Sciences, New York University, New York, NY

Huy Tuan Pham

Stanford University, Stanford, CA