The magical Ewens sampling formula
The magical Ewens sampling formula
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神奇的埃文斯采样公式
DOI：
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发表时间：
2021
影响因子：
0.9
通讯作者：
S. Tavaré
中科院分区：
文献类型：
--
作者：
S. Tavaré
从n条煮熟的意大利面条开始，随机选择两端绑在一起，制作一组意大利面条圈。期望的篮球数是多少？关于长度为1、2、.的圈数的分布可以说些什么？当n很大时，最长环的行为是什么？所有的环都有不同长度的概率是多少？像这样的问题在数学的许多领域以各种形式出现，其中一个联系是它们与Ewens抽样公式（ESF）的关系。我将描述一些相关的例子，包括素因子分解，随机映射和随机置换，说明ESF所发挥的核心作用。我还将讨论利用ESF世界的另一个奇迹，即Feller耦合（FC）来模拟可分解组合结构的方法。对意大利面条游戏的分析表明，明显偏离FC的微小偏差可能会引发许多未解决的问题。伦敦数学学会（LMS）的几位前任主席都对ESF的理论做出了贡献，我将在下面举例说明。
Starting with n cooked spaghetti strands, tie randomly chosen ends together to produce a collection of spaghetti hoops. What is the expected number of hoops? What can be said about the distribution of the number of hoops of length 1, 2, ...? What is the behaviour of the longest hoops when n is large? What is the probability that all the hoops have different lengths? Questions like these appear in many guises in many areas of mathematics, one connection being their relation to the Ewens sampling formula (ESF). I will describe a number of related examples, including prime factorisation, random mappings and random permutations, illustrating the central role played by the ESF. I will also discuss methods for simulating decomposable combinatorial structures by exploiting another wonder of the ESF world, namely the Feller coupling (FC). Analysis of the spaghetti game in which ends of different strands must be tied shows that apparently small departures from the FC can open up a number of unsolved problems. Several past presidents of the London Mathematical Society (LMS) have contributed to the theory around the ESF, as I will illustrate.
用于随机紊乱的 Feller 联轴器
影响因子：
1.4
作者：
da Silva, Poly H.;Jamshidpey, Arash;Tavaré, Simon
通讯作者：
Tavaré, Simon