On the discrepancy of random low degree set systems

Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are n elements and m sets and each element lies in t randomly chosen sets. In this setting, Ezra and Lovett showed an O((t log t)1/2) discrepancy bound in the regime when n ≤ m and an O(1) bound when n 3 » mt. In this paper, we give a tight [MATH...More