{"title":"具有固定参数的Laguerre过程的缠绕特性","authors":"Alexander I. Bufetov, Yosuke Kawamoto","doi":"10.1007/s10955-025-03441-w","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate the intertwining of Laguerre processes of parameter <span>\\(\\alpha \\)</span> in different dimensions. We introduce a Feller kernel that depends on <span>\\(\\alpha \\)</span> and intertwines the <span>\\(\\alpha \\)</span>-Laguerre process in <span>\\(N+1\\)</span> dimensions and that in <i>N</i> dimensions. When <span>\\(\\alpha \\)</span> is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order <span>\\((N+\\alpha +1) \\times (N+1)\\)</span> are fixed, then the those of its <span>\\((N+\\alpha ) \\times N \\)</span> truncation matrix are given by the new kernel.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03441-w.pdf","citationCount":"0","resultStr":"{\"title\":\"The Intertwining Property for Laguerre Processes with a Fixed Parameter\",\"authors\":\"Alexander I. Bufetov, Yosuke Kawamoto\",\"doi\":\"10.1007/s10955-025-03441-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We investigate the intertwining of Laguerre processes of parameter <span>\\\\(\\\\alpha \\\\)</span> in different dimensions. We introduce a Feller kernel that depends on <span>\\\\(\\\\alpha \\\\)</span> and intertwines the <span>\\\\(\\\\alpha \\\\)</span>-Laguerre process in <span>\\\\(N+1\\\\)</span> dimensions and that in <i>N</i> dimensions. When <span>\\\\(\\\\alpha \\\\)</span> is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order <span>\\\\((N+\\\\alpha +1) \\\\times (N+1)\\\\)</span> are fixed, then the those of its <span>\\\\((N+\\\\alpha ) \\\\times N \\\\)</span> truncation matrix are given by the new kernel.</p></div>\",\"PeriodicalId\":667,\"journal\":{\"name\":\"Journal of Statistical Physics\",\"volume\":\"192 5\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-04-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10955-025-03441-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10955-025-03441-w\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-025-03441-w","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
The Intertwining Property for Laguerre Processes with a Fixed Parameter
We investigate the intertwining of Laguerre processes of parameter \(\alpha \) in different dimensions. We introduce a Feller kernel that depends on \(\alpha \) and intertwines the \(\alpha \)-Laguerre process in \(N+1\) dimensions and that in N dimensions. When \(\alpha \) is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order \((N+\alpha +1) \times (N+1)\) are fixed, then the those of its \((N+\alpha ) \times N \) truncation matrix are given by the new kernel.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.