A new SDP-guided Brownian-rounding technique, decoupling via affine spectral-independence, proves discrepancy O(√k) for degree-k set systems with k ≥ log² n and Õ(log^{1/4} n) for unit-norm matrices.
Balancing vectors and G aussian measures of n-dimensional convex bodies
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Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\'os Bounds Beyond Banaszczyk
A new SDP-guided Brownian-rounding technique, decoupling via affine spectral-independence, proves discrepancy O(√k) for degree-k set systems with k ≥ log² n and Õ(log^{1/4} n) for unit-norm matrices.