Khinchin型不等式经由Hadamard分解
Khinchin-type inequalities via Hadamard's factorisation
AI总结：
本文通过Hadamard分解定理和Newton不等式，证明了L型随机变量所有偶数阶矩的Khinchin型不等式，并处理了铁磁依赖情形，同时比较了相关概念。
摘要：
我们证明了对于L型随机变量和所有偶数阶矩，具有锐利常数的Khinchin型不等式。我们的主要工具是来自复分析的Hadamard分解定理，结合初等对称函数的Newton不等式。除了独立求和项的情形，我们还处理了非负外磁场中的铁磁依赖（得益于Newman对Lee-Yang定理的推广）。最后，我们比较了L型、超亚高斯性（由Nayar和Oleszkiewicz引入）和强对数凹性（由Gurvits引入）的概念，其中后两者是等价的。
英文摘要：
We prove Khinchin-type inequalities with sharp constants for type L random variables and all even moments. Our main tool is Hadamard's factorisation theorem from complex analysis, combined with Newton's inequalities for elementary symmetric functions. Besides the case of independent summands, we also treat ferromagnetic dependencies in a nonnegative external magnetic field (thanks to Newman's generalisation of the Lee-Yang theorem). Lastly, we compare the notions of type L, ultra sub-Gaussianity (introduced by Nayar and Oleszkiewicz) and strong log-concavity (introduced by Gurvits), with the latter two being equivalent.
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