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

06/17/2022

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by   Afonso S. Bandeira, et al.

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In this expository note, we discuss an early partial coloring result of B. Kashin [C. R. Acad. Bulgare Sci., 1985]. Although this result only implies Spencer's six standard deviations [Trans. Amer. Math. Soc., 1985] up to a loglog n factor, Kashin's argument gives a simple proof of the existence of a constant discrepancy partial coloring in the setup of Komlós conjecture.