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arXiv · 2402.10504

Resilience of Rademacher chaos of low degree

Elad Aigner-Horev·Daniel Rosenberg·Roi Weiss
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Abstract

The {\em resilience} of a Rademacher chaos is the maximum number of adversarial sign-flips that the chaos can sustain without having its largest atom probability significantly altered. Inspired by probabilistic lower-bound guarantees for the resilience of linear Rademacher chaos (aka. resilience of the Littlewood-Offord problem), obtained by Bandeira, Ferber, and Kwan (Advances in Mathematics, Vol. $319$, $2017$), we provide probabilistic lower-bound guarantees for the resilience of Rademacher chaos of arbitrary degree; these being most meaningful provided that the degree is constant.

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Elad Aigner-Horev, Daniel Rosenberg, Roi Weiss. 2024-02-16. Resilience of Rademacher chaos of low degree. https://arxiv.org/abs/2402.10504

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