{"title":"关于Haar酉矩阵的部分转置","authors":"J. Mingo, M. Popa, K. Szpojankowski","doi":"10.4064/sm210517-13-12","DOIUrl":null,"url":null,"abstract":"We consider the effect of a partial transpose on the limit ∗-distribution of a Haar distributed random unitary matrix. If we fix the number of blocks, b, we show that the partial transpose can be decomposed along diagonals into a sum of b matrices which are asymptotically free and identically distributed. We then consider the joint effect of different block decompositions and show that under some mild assumptions we also get asymptotic freeness.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the partial transpose of a Haar unitary matrix\",\"authors\":\"J. Mingo, M. Popa, K. Szpojankowski\",\"doi\":\"10.4064/sm210517-13-12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the effect of a partial transpose on the limit ∗-distribution of a Haar distributed random unitary matrix. If we fix the number of blocks, b, we show that the partial transpose can be decomposed along diagonals into a sum of b matrices which are asymptotically free and identically distributed. We then consider the joint effect of different block decompositions and show that under some mild assumptions we also get asymptotic freeness.\",\"PeriodicalId\":51179,\"journal\":{\"name\":\"Studia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/sm210517-13-12\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm210517-13-12","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider the effect of a partial transpose on the limit ∗-distribution of a Haar distributed random unitary matrix. If we fix the number of blocks, b, we show that the partial transpose can be decomposed along diagonals into a sum of b matrices which are asymptotically free and identically distributed. We then consider the joint effect of different block decompositions and show that under some mild assumptions we also get asymptotic freeness.
期刊介绍:
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.