Condensation and Extremes for a Fluctuating Number of Independent Random Variables
Condensation and Extremes for a Fluctuating Number of Independent Random Variables
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波动数量的独立随机变量的凝聚和极值
DOI：
10.1007/s10955-020-02679-w
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发表时间：
2020
影响因子：
1.6
通讯作者：
C. Godrèche
中科院分区：
文献类型：
--
作者：
C. Godrèche
我们讨论了三类密切相关的随机过程的凝结和极值问题：(a)随机分配模型和零范围过程，(b)捆绑更新过程，(c)自由更新过程。对于前一类，系统的组成部分的数量是固定的，而对于另外两类，它是一个波动的数量。对这些主题的研究分散在文献中，通常披着其他外衣。我们用独立随机变量和的语言对这个问题作了一个简明扼要的说明，以便我们不需要考虑特定的模型，并强调其要点。除了给出理论的统一呈现外，这项工作还调查了迄今为止在以前的研究中尚未探索的方面。具体来说，我们展示了随机分配模型和零范围过程的研究如何作为研究其他两类过程的背景，这些过程是当前工作约束和自由更新过程的核心。然后，我们提出了对这三类过程的极值统计的新见解，从而可以更深入地理解冷凝机制和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.
影响因子：
1.4
作者：
In'es Armend'ariz;S. Grosskinsky;M. Loulakis
通讯作者：
In'es Armend'ariz;S. Grosskinsky;M. Loulakis
热力学极限内冷凝零范围过程的亚稳定性
影响因子：
2
作者：
Armendáriz I
通讯作者：
Armendáriz I