Dickman分布的逼近与拟对数组合结构
Approximation by the Dickman distribution and quasi-logarithmic combinatorial structures
摘要：
拟对数组合结构是一类可分解的组合结构，它扩展了Arratia，Barnival和Tavaré（2003）所考虑的对数类。为了获得其分量谱的渐近近似，首先必须根据Dickman分布建立独立随机变量的相关序列之和的近似。这反过来又需要一个论点，通过引入阻塞结构来细化Mineka耦合，从而导致所讨论的总和的耦合率呈指数级急剧上升。应用程序包括分布极限定理的最大组件的大小和准对数组合结构中的小组件的计数向量。
英文摘要：
Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavaré (2003). In order to obtain asymptotic approximations to their component spectrum, it is necessary first to establish an approximation to the sum of an associated sequence of independent random variables in terms of the Dickman distribution. This in turn requires an argument that refines the Mineka coupling by incorporating a blocking construction, leading to exponentially sharper coupling rates for the sums in question. Applications include distributional limit theorems for the size of the largest component and for the vector of counts of the small components in a quasi-logarithmic combinatorial structure.
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