论文标题
随机排列中下降数量的急剧大偏差和浓度不平等
Sharp large deviations and concentration inequalities for the number of descents in a random permutation
论文作者
论文摘要
本文的目的是进一步分析随机排列中下降数量的行为。通过依靠合适的Martingale分解或Irwin-Hall分布的两种不同方法，我们证明了下降的数量满足了急剧的较大偏差原理。还提供了涉及大偏差原理中速率函数的非常精确的浓度不平等。
The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin-Hall distribution, we prove that the number of descents satisfies a sharp large deviation principle. A very precise concentration inequality involving the rate function in the large deviation principle is also provided.
