Note on a Conjecture of Talagrand: Expectation Thresholds vs. Fractional Expectation Thresholds

Abstract

We show that a restricted version of a conjecture of M. Talagrand on the relation between "expectation thresholds" and "fractional expectation thresholds" follows easily from a strong version of a second conjecture of Talagrand, on "selector processes". The selector process conjecture was proved by Park and Pham, and the quantitative strengthening used here is due to Bednorz, Martynek, and Meller.