2024/12/28 by С. В. Асташкин, Astashkin, Sergey V., Константин Владимирович Лыков +1
Mathematics · #05C35 #46E30 #FOS: Mathematics #Mathematical Approximation and Integration #Primary 46B09 #Probability (math.PR) #Secondary 05C15
paper · pdf · doi:10.48550/arxiv.2412.20107
openalex publication_date 2024/12/28 · openalex created_date 2025/01/01 · openalex updated_date 2026/07/28
We prove that both multiple Rademacher system and Rademacher chaos possess the property of random unconditional convergence in the space L_∞. This fact combined with some intimate connections between L_∞-norms of linear combinations of elements of these systems and some special norms of matrices of their coefficients allows us to establish 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 for the unweighted case.