在随机矩阵的秩上

Random Struct. Algorithms Pub Date : 2000-03-01 DOI:10.1002/(SICI)1098-2418(200003)16:2%3C209::AID-RSA6%3E3.0.CO;2-1

C. Cooper

{"title":"在随机矩阵的秩上","authors":"C. Cooper","doi":"10.1002/(SICI)1098-2418(200003)16:2%3C209::AID-RSA6%3E3.0.CO;2-1","DOIUrl":null,"url":null,"abstract":"Let M=(mij) be a random n×n matrix over GF(2). Each matrix entry mij is independently and identically distributed, with Pr(mij=0)=1−p(n) and Pr(mij=1)=p(n). The probability that the matrix M is nonsingular tends to c2≈0.28879 provided min(p, 1−p)≥(log n+d(n))/n for any d(n)∞. Sharp thresholds are also obtained for constant d(n). This answers a question posed in a paper by J. Blomer, R. Karp, and E. Welzl (Random Struct Alg, 10(4) (1997)). ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 209–232, 2000","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"2000 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"83","resultStr":"{\"title\":\"On the rank of random matrices\",\"authors\":\"C. Cooper\",\"doi\":\"10.1002/(SICI)1098-2418(200003)16:2%3C209::AID-RSA6%3E3.0.CO;2-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let M=(mij) be a random n×n matrix over GF(2). Each matrix entry mij is independently and identically distributed, with Pr(mij=0)=1−p(n) and Pr(mij=1)=p(n). The probability that the matrix M is nonsingular tends to c2≈0.28879 provided min(p, 1−p)≥(log n+d(n))/n for any d(n)∞. Sharp thresholds are also obtained for constant d(n). This answers a question posed in a paper by J. Blomer, R. Karp, and E. Welzl (Random Struct Alg, 10(4) (1997)). ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 209–232, 2000\",\"PeriodicalId\":303496,\"journal\":{\"name\":\"Random Struct. Algorithms\",\"volume\":\"2000 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"83\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Struct. Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/(SICI)1098-2418(200003)16:2%3C209::AID-RSA6%3E3.0.CO;2-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(200003)16:2%3C209::AID-RSA6%3E3.0.CO;2-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 83

摘要

设M=(mij)是GF(2)上的随机n×n矩阵。每个矩阵项mij是独立同分布的，Pr(mij=0)=1−p(n)， Pr(mij=1)=p(n)。对于任意d(n)∞，当min(p, 1−p)≥(log n+d(n))/n时，矩阵M非奇异的概率趋于c2≈0.28879。对于恒定的d(n)，也可以得到明显的阈值。这回答了J. Blomer, R. Karp和E. Welzl (Random Struct Alg, 10(4)(1997))在一篇论文中提出的问题。©2000 John Wiley & Sons, Inc随机结构。Alg。中文信息学报，16,209 - 232,2000

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the rank of random matrices

Let M=(mij) be a random n×n matrix over GF(2). Each matrix entry mij is independently and identically distributed, with Pr(mij=0)=1−p(n) and Pr(mij=1)=p(n). The probability that the matrix M is nonsingular tends to c2≈0.28879 provided min(p, 1−p)≥(log n+d(n))/n for any d(n)∞. Sharp thresholds are also obtained for constant d(n). This answers a question posed in a paper by J. Blomer, R. Karp, and E. Welzl (Random Struct Alg, 10(4) (1997)). ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 209–232, 2000

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Random Struct. Algorithms

自引率

0.00%

发文量