Cumulants, concentration and superconcentration

科学网络累积量、集中度和超集中度集中在研究地点柏林、波鸿、明斯特和奥斯纳布吕克的九名年轻科学家的共同兴趣上。这三个主题在当前概率论的几个研究领域中是基本的。科学网络第一阶段的主要重点是一方面探索经典累积量方法的新应用，以证明集中不平等或中等偏差。另一方面，技术工具的描述分散在文献中，应该在一篇调查文章中汇集在一起。我们借此机会审查给定假设的最佳性，并使其适应新的应用。此外，在第二阶段，我们选择了超浓缩这一非常年轻的研究课题，并对伴随着超浓缩现象的标准有了更深的理解。为此，我们成立了较小的工作组，并在申请者的国内机构举办了五个重点讲习班。一组杰出的国际专家将陪同这一方案，并将为进一步研究提供新的投入。

The scientific network cumulants, concentration and superconcentration focuses on the common interests of nine young scientists at the research locations Berlin, Bochum, Münster and Osnabrück. The three topics are fundamental in several research areas in current probability theory. The main focus of the first phase of the scientific network is on the one hand to explore new applications of the classical method of cumulants to prove concentration inequalities or moderate deviations. On the other hand the technical tools whose descriptions are scattered throughout the literature should be brought together in an survey article. We take this opportunity to review the optimality of the given assumptions and adapt them to new applications. Moreover, in a second phase we pick up the very young research topic of superconcentration and develop a deeper understanding of criteria accompanying the phenomenon of superconcentration. For this purpose we form smaller working groups and implement five focused workshops at the home institutions of the applicants. A group of distinguished international experts will accompany this programme and will give fresh input for further research.