论文标题
比较真实对数符号随机变量的矩
Comparing moments of real log-concave random variables
论文作者
论文摘要
我们表明，对于每一个平均零log-concave real andan andant变量$ x $一个一个$ \ | x \ | _p \ leq \ leq \ frac {p} {q} {q} \ | x \ | x \ | _q $ for $ p \ geq q \ ge q \ geq 1 $，超出了众所周知的符号随机变量。我们还证明，在任意log-concave的类别中，对于$ p> q> q> 0 $数量$ \ | x \ | _p / \ | x \ | _q $，对于某些移动的指数分布而言，最大化。在此基础上，我们得出了绑定的$ \ | x \ | _p \ leq c_0 \ frac {p} {q} {q} \ | x \ | x \ | _q $，用于任意log-concave $ x $，具有绝对可能的绝对常数$ c_0 = e^（1/e）$ c_0 = e^（1/e）}代表兰伯特功能。
We show that for every mean zero log-concave real random variable $X$ one has $\|X\|_p \leq \frac{p}{q} \|X\|_q$ for $p \geq q \geq 1$, going beyond the well-known case of symmetric random variables. We also prove that in the class of arbitrary log-concave real random variables for $p>q > 0$ the quantity $\|X\|_p / \|X\|_q$ is maximized for some shifted exponential distribution. Building upon this we derive the bound $\|X\|_p \leq C_0 \frac{p}{q} \|X\|_q$ for arbitrary log-concave $X$, with best possible absolute constant $C_0=e^{W(1/e)} \approx 1.3211$ in front of $\frac{p}{q}$, where $W$ stands for the Lambert function.
