D. Shlyakhtenko, Terence Tao. With an appendix by David Jekel
{"title":"分数自由卷积幂","authors":"D. Shlyakhtenko, Terence Tao. With an appendix by David Jekel","doi":"10.1512/iumj.2022.71.9163","DOIUrl":null,"url":null,"abstract":"The extension $k \\mapsto \\mu^{\\boxplus k}$ of the concept of a free convolution power to the case of non-integer $k \\geq 1$ was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory. In this paper we give two proofs of the monotonicity of the free entropy and free Fisher information of the (normalized) free convolution power in this continuous setting, and also establish an intriguing variational description of this process.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Fractional free convolution powers\",\"authors\":\"D. Shlyakhtenko, Terence Tao. With an appendix by David Jekel\",\"doi\":\"10.1512/iumj.2022.71.9163\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The extension $k \\\\mapsto \\\\mu^{\\\\boxplus k}$ of the concept of a free convolution power to the case of non-integer $k \\\\geq 1$ was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory. In this paper we give two proofs of the monotonicity of the free entropy and free Fisher information of the (normalized) free convolution power in this continuous setting, and also establish an intriguing variational description of this process.\",\"PeriodicalId\":50369,\"journal\":{\"name\":\"Indiana University Mathematics Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2020-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indiana University Mathematics Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1512/iumj.2022.71.9163\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indiana University Mathematics Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1512/iumj.2022.71.9163","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The extension $k \mapsto \mu^{\boxplus k}$ of the concept of a free convolution power to the case of non-integer $k \geq 1$ was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory. In this paper we give two proofs of the monotonicity of the free entropy and free Fisher information of the (normalized) free convolution power in this continuous setting, and also establish an intriguing variational description of this process.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
