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About this paper
Nicola Wengiel
The paper proves a worst-case lower bound for two-color discrepancy of axis-parallel boxes in fixed dimensions d≥3. It constructs point sets and test functions that force imbalance under every coloring, using hereditary discrepancy and a Gaussian small-ball argument. The bound is c_d(log N)^(d−1/2), matching Nikolov’s upper bound; Wei’s separate result covers d=2.
Summary by alphaXiv.
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