{"title":"关于乘积替换算法的变体","authors":"C.R. Leedham-Green","doi":"10.1017/s0017089523000435","DOIUrl":null,"url":null,"abstract":"We discuss a variant, named ‘Rattle’, of the product replacement algorithm. Rattle is a Markov chain, that returns a random element of a black box group. The limiting distribution of the element returned is the uniform distribution. We prove that, if the generating sequence is long enough, the probability distribution of the element returned converges unexpectedly quickly to the uniform distribution.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"20 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a variant of the product replacement algorithm\",\"authors\":\"C.R. Leedham-Green\",\"doi\":\"10.1017/s0017089523000435\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss a variant, named ‘Rattle’, of the product replacement algorithm. Rattle is a Markov chain, that returns a random element of a black box group. The limiting distribution of the element returned is the uniform distribution. We prove that, if the generating sequence is long enough, the probability distribution of the element returned converges unexpectedly quickly to the uniform distribution.\",\"PeriodicalId\":50417,\"journal\":{\"name\":\"Glasgow Mathematical Journal\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Glasgow Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0017089523000435\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasgow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0017089523000435","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We discuss a variant, named ‘Rattle’, of the product replacement algorithm. Rattle is a Markov chain, that returns a random element of a black box group. The limiting distribution of the element returned is the uniform distribution. We prove that, if the generating sequence is long enough, the probability distribution of the element returned converges unexpectedly quickly to the uniform distribution.
期刊介绍：
Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics.
The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.
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