Random unconditional convergence of Rademacher chaos in $L_\infty $ and sharp estimates for discrepancy of weighted graphs and hypergraphs

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2025年8月13日

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Sergey V. Astashkin,
Konstantin V. Lykov

摘要

We prove that both multiple Rademacher system and Rademacher chaos possess the property of random unconditional convergence in the space $L_\infty $ $L_{\infty}$ . This fact combined with some intimate connections between $L_\infty $ $L_{\infty}$ -norms of linear combinations of elements of these systems and some special norms of matrices of their coefficients allows us to establish novel sharp two-sided estimates for the discrepancy of edge-weighted graphs and hypergraphs. Some of these results extend the classical theorem proved by Erdös and Spencer in the unweighted case.

Random unconditional convergence of Rademacher chaos in \(L_\infty \) and sharp estimates for discrepancy of weighted graphs and hypergraphs

摘要