On the discrepancy of random low degree set systems

RANDOM STRUCTURES & ALGORITHMS, pp. 695.0-705.0, 2020.

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Abstract:

Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there arenelements andmsets and each element lies intrandomly chosen sets. In this setting, Ezra and Lovett showed anO((tlogt)1/2)discrepancy bound whenn <= mand anO(1) bound whenn >> m(t). In this paper, we give a tightO(t)bound for the entire range o...More

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