Some Explorations on Two Conjectures About Rademacher Sequences
查看参考文献15篇
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文摘
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qIn this paper, we explore two conjectures about Rademacher sequences. Let(ε_i)be a Rademacher sequence, i.e., a sequence of independent {-1, 1}-valued symmetric random variables. Set S_n = a_1ε_1+···+a_nε_n for a =(a_1, ···, a_n)∈ R~n. The first conjecture says that P(|S_n| ≤ ∥a∥)≥ 1/2 for all a ∈ R~n and n ∈ N. The second conjecture says that P(|S_n| ≥ ∥a∥)≥ 7/32 for all a ∈ R~n and n ∈ N. Regarding the first conjecture, we present several new equivalent formulations. These include a topological view, a combinatorial version and a strengthened version of the conjecture. Regarding the second conjecture, we prove that it holds true when n ≤ 7. |
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来源
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Acta Mathematicae Applicatae Sinica-English Series
,2021,37(1):1-16 【核心库】
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DOI
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10.1007/s10255-021-0993-0
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关键词
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Rademacher sequence
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Tomaszewaki's constant
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Hitczenko and Kwapien's constant
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地址
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1.
College of Mathematics, Sichuan University, Chengdu, 610065
2.
School of Economics and Statistics, Guangzhou University, Guangzhou, 510006
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Department of Mathematics and Statistics, Concordia University, Canada, Montreal, H3G 1M8
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语种
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英文 |
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文献类型
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研究性论文 |
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ISSN
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0168-9673 |
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学科
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数学 |
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基金
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国家自然科学基金
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国家留学基金委员会（CSC）项目
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加拿大自然科学与工程研究理事会（NSERC）项目
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文献收藏号
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CSCD:6915535
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参考文献 共
15
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