{"title":"极限周期介质中的均匀安德森定位和非局部迷你型估算","authors":"V. Chulaevsky, Y. Suhov","doi":"10.61102/1024-2953-mprf.2023.29.4.004","DOIUrl":null,"url":null,"abstract":"We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class of limit-periodic lattice Schr¨odinger operators. An important ingredient of the proof is a generalized variant of the well-known Minami estimates (correlation inequalities for the eigenvalues) to the case where the spectral intervals can be arbitrarily placed in the real line. The new corre- lation inequalities allow us to substantially simplify and make more transparent the application of the KAM (Kolmogorov-Arnold-Moser) techniques.","PeriodicalId":48890,"journal":{"name":"Markov Processes and Related Fields","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uniform Anderson Localization and Non-local Minami-type Estimates in Limit-periodic Media\",\"authors\":\"V. Chulaevsky, Y. Suhov\",\"doi\":\"10.61102/1024-2953-mprf.2023.29.4.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class of limit-periodic lattice Schr¨odinger operators. An important ingredient of the proof is a generalized variant of the well-known Minami estimates (correlation inequalities for the eigenvalues) to the case where the spectral intervals can be arbitrarily placed in the real line. The new corre- lation inequalities allow us to substantially simplify and make more transparent the application of the KAM (Kolmogorov-Arnold-Moser) techniques.\",\"PeriodicalId\":48890,\"journal\":{\"name\":\"Markov Processes and Related Fields\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Markov Processes and Related Fields\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.61102/1024-2953-mprf.2023.29.4.004\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Markov Processes and Related Fields","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.61102/1024-2953-mprf.2023.29.4.004","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Uniform Anderson Localization and Non-local Minami-type Estimates in Limit-periodic Media
We prove a uniform exponential localization of eigenfunctions and simplicity of spectrum for a class of limit-periodic lattice Schr¨odinger operators. An important ingredient of the proof is a generalized variant of the well-known Minami estimates (correlation inequalities for the eigenvalues) to the case where the spectral intervals can be arbitrarily placed in the real line. The new corre- lation inequalities allow us to substantially simplify and make more transparent the application of the KAM (Kolmogorov-Arnold-Moser) techniques.
期刊介绍:
Markov Processes And Related Fields
The Journal focuses on mathematical modelling of today''s enormous wealth of problems from modern technology, like artificial intelligence, large scale networks, data bases, parallel simulation, computer architectures, etc.
Research papers, reviews, tutorial papers and additionally short explanations of new applied fields and new mathematical problems in the above fields are welcome.