论文标题
凝结和极端数量的独立随机变量的极端
Condensation and extremes for a fluctuating number of independent random variables
论文作者
论文摘要
我们解决了三类纯粹相关随机过程的凝结和极端问题：（a）随机分配模型和零范围的过程，（b）绑定的续订过程，（c）自由续订过程。对于前类，系统的组件数量是固定的，但对于其他两个类，是一个波动的数量。这些主题的研究散布在文献中，通常穿着其他衣服打扮。我们用独立随机变量的总和的语言对主题进行了剥离，以释放自己考虑特定模型并强调必需品。除了给出理论的统一介绍外，这项工作还研究了到目前为止在先前研究中尚未探索的方面。具体而言，我们展示了如何研究随机分配模型和零范围过程的研究，可以作为研究目前工作中心的其他两个类别的过程的背景 - 绑扎和自由续订过程。然后，我们对这三类过程的极值统计数据提供了新的见解，这些统计数据可以更深入地了解冷凝机制以及对冷凝物波动的定量分析。
We address the question of condensation and extremes for three classes of intimately related stochastic processes: (a) random allocation models and zero-range processes, (b) tied-down renewal processes, (c) free renewal processes. While for the former class the number of components of the system is fixed, for the two other classes it is a fluctuating quantity. Studies of these topics are scattered in the literature and usually dressed up in other clothing. We give a stripped-down account of the subject in the language of sums of independent random variables in order to free ourselves of the consideration of particular models and highlight the essentials. Besides giving a unified presentation of the theory, this work investigates facets so far unexplored in previous studies. Specifically, we show how the study of the class of random allocation models and zero-range processes can serve as a backdrop for the study of the two other classes of processes central to the present work -- tied-down and free renewal processes. We then present new insights on the extreme value statistics of these three classes of processes which allow a deeper understanding of the mechanism of condensation and the quantitative analysis of the fluctuations of the condensate.
