高斯过程上确界及随机乘性函数和的Ω结果
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
摘要：
证明了高斯过程上确界的上尾概率的新的下界。与许多现有的界限，我们的结果是不渐近的，但提供强有力的信息时，只有一点点进入上尾。我们提出了一个扩展的应用高斯版本的随机过程研究Halasz。这就大大改进了随机乘性函数和的下界结果。我们进一步说明了我们的方法，通过改进下界的一些经典常数极值理论，Pickands常数$H_α$，作为$α\rightarrow 0$。
英文摘要：
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We present an extended application to a Gaussian version of a random process studied by Halasz. This leads to much improved lower bound results for the sum of a random multiplicative function. We further illustrate our methods by improving lower bounds for some classical constants from extreme value theory, the Pickands constants $H_α$, as $α\rightarrow 0$.
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