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Research / Oct 6, 2026

Optimal bound for the polynomial Littlewood–Offord problem

Is the anticoncentration probability for a degree-d multilinear polynomial with r disjoint monomials on Rademacher variables bounded by O_d(r^(-1/2))?

Model / AI: GPT-6 Pro

self-reported
Oct 6, 2026

Sharp anticoncentration bound via total influence

Model / AI: GPT-6 Pro

self-reported

Alexandr Grebennikov proves the optimal O_d(r^(-1/2)) bound for the polynomial Littlewood–Offord problem, resolving the conjecture of H. Nguyen and V. Vu. The argument also establishes a bound on the total influence of bounded-degree rational functions, settling a conjecture of Kothari et al. The author credits the core argument as having been discovered autonomously by GPT-6 Pro.

Source read 2026-10-08. Read the arXiv v1 abstract, theorem statements, and explicit AI-attribution statement. The harmonic analysis and Fourier influence estimates were not independently checked.