{"title":"双线性索引随机过程——完全提升插值的\\emph{平稳化}","authors":"Mihailo Stojnic","doi":"arxiv-2311.18097","DOIUrl":null,"url":null,"abstract":"Our companion paper \\cite{Stojnicnflgscompyx23} introduced a very powerful\n\\emph{fully lifted} (fl) statistical interpolating/comparison mechanism for\nbilinearly indexed random processes. Here, we present a particular realization\nof such fl mechanism that relies on a stationarization along the interpolating\npath concept. A collection of very fundamental relations among the\ninterpolating parameters is uncovered, contextualized, and presented. As a nice\nbonus, in particular special cases, we show that the introduced machinery\nallows various simplifications to forms readily usable in practice. Given how\nmany well known random structures and optimization problems critically rely on\nthe results of the type considered here, the range of applications is pretty\nmuch unlimited. We briefly point to some of these opportunities as well.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"86 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bilinearly indexed random processes -- \\\\emph{stationarization} of fully lifted interpolation\",\"authors\":\"Mihailo Stojnic\",\"doi\":\"arxiv-2311.18097\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Our companion paper \\\\cite{Stojnicnflgscompyx23} introduced a very powerful\\n\\\\emph{fully lifted} (fl) statistical interpolating/comparison mechanism for\\nbilinearly indexed random processes. Here, we present a particular realization\\nof such fl mechanism that relies on a stationarization along the interpolating\\npath concept. A collection of very fundamental relations among the\\ninterpolating parameters is uncovered, contextualized, and presented. As a nice\\nbonus, in particular special cases, we show that the introduced machinery\\nallows various simplifications to forms readily usable in practice. Given how\\nmany well known random structures and optimization problems critically rely on\\nthe results of the type considered here, the range of applications is pretty\\nmuch unlimited. We briefly point to some of these opportunities as well.\",\"PeriodicalId\":501330,\"journal\":{\"name\":\"arXiv - MATH - Statistics Theory\",\"volume\":\"86 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2311.18097\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2311.18097","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bilinearly indexed random processes -- \emph{stationarization} of fully lifted interpolation
Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful
\emph{fully lifted} (fl) statistical interpolating/comparison mechanism for
bilinearly indexed random processes. Here, we present a particular realization
of such fl mechanism that relies on a stationarization along the interpolating
path concept. A collection of very fundamental relations among the
interpolating parameters is uncovered, contextualized, and presented. As a nice
bonus, in particular special cases, we show that the introduced machinery
allows various simplifications to forms readily usable in practice. Given how
many well known random structures and optimization problems critically rely on
the results of the type considered here, the range of applications is pretty
much unlimited. We briefly point to some of these opportunities as well.