发表机构
Institute of Mathematics, University of Warsaw（华沙大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对具有正则矩增长的独立对称随机变量生成的任意阶解耦混沌，给出仅依赖系数张量和一维尾部的双边矩估计，证明基于划分范数、高斯平滑与乘积比较，并补充尾部界及显式公式。
AI 中文摘要
我们给出了由具有正则矩增长的独立对称随机变量生成的任意阶解耦混沌的双边矩估计：对每个 $p\ge1$，有 $\\|X\\|_{2p}\le K\\|X\\|_p$。这些估计仅涉及系数张量和一维尾部。它们使用了 Adamczak 和 Latała 的划分范数，常数仅依赖于阶数和 $K$。证明从对数凹尾部开始。高斯平滑给出了归纳所需的期望范数的估计，而乘积比较将剩余分布归约到这种情况。比较引入的额外张量指标通过 Rademacher 矩被移除。与对数凹尾部变量的乘积进行比较后，公式扩展到正则矩增长。我们还给出了尾部界以及 $r\ge1$ 的显式 Rademacher 和 Weibull 公式，包括四阶例子。本文在 GPT Astra-6 的协助下完成。
英文摘要
We give two-sided moment estimates for decoupled chaoses of any order generated by independent symmetric random variables with regular moment growth: $\|X\|_{2p}\le K\|X\|_p$ for every $p\ge1$. The estimates involve only the coefficient tensor and the one-dimensional tails. They use the partition norms of Adamczak and Latała, with constants depending only on the order and on $K$. The proof starts with log-concave tails. Gaussian smoothing gives the estimate for the expected norm needed for induction, and a product comparison reduces the remaining distributions to this case. The extra tensor indices introduced by the comparison are removed using Rademacher moments. A comparison with products of log-concave-tail variables then extends the formula to regular moment growth. We also give tail bounds and explicit Rademacher and Weibull formulas for $r\ge1$, including fourth-order examples. This article was developed with the assistance of GPT Astra-6.
CommentsThis article was developed with the assistance of GPT Astra-6
