论文标题
霍尔德的不平等及其反向概率的观点
Hölder's inequality and its reverse-a probabilistic point of view
论文作者
论文摘要
在本文中，我们考虑了Hölder的不平等现象，考虑到经典的Hölder不平等中的术语比例比$ \ mathbb {r}^n $中的随机矢量。我们证明了该比率的中心限制定理，然后使我们能够以高概率将不等式扭转至乘法常数。随机性的模型包括$ \ ell_p^n $球和球体上的均匀分布。我们还提供了浆果 - 埃森类型的结果，并证明了适当归一化的Hölder比率的大且中等的偏差原理。
In this article we take a probabilistic look at Hölder's inequality, considering the ratio of terms in the classical Hölder inequality for random vectors in $\mathbb{R}^n$. We prove a central limit theorem for this ratio, which then allows us to reverse the inequality up to a multiplicative constant with high probability. The models of randomness include the uniform distribution on $\ell_p^n$ balls and spheres. We also provide a Berry-Esseen type result and prove a large and a moderate deviation principle for the suitably normalized Hölder ratio.
