A remark on Kashin’s discrepancy argument and partial coloring in the Komlós conjecture

Abstract

In this expository note, we discuss an early partial coloring result of B. Kashin (1985). Although this result only implies Spencer’s six standard deviations (1985) up to a $\log \log n$ factor, Kashin’s argument gives a simple proof of the existence of a constant discrepancy partial coloring in the setup of the Komlós conjecture.