{"title":"Hölder continuity of the integrated density of states for Liouville frequencies","authors":"Rui Han, Wilhelm Schlag","doi":"arxiv-2408.15962","DOIUrl":null,"url":null,"abstract":"We prove H\\\"older continuity of the Lyapunov exponent $L(\\omega,E)$ and the\nintegrated density of states at energies that satisfy\n$L(\\omega,E)>4\\kappa(\\omega,E)\\cdot \\beta(\\omega)\\geq 0$ for general analytic\npotentials, with $\\kappa(\\omega,E)$ being Avila's acceleration.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15962","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove H\"older continuity of the Lyapunov exponent $L(\omega,E)$ and the
integrated density of states at energies that satisfy
$L(\omega,E)>4\kappa(\omega,E)\cdot \beta(\omega)\geq 0$ for general analytic
potentials, with $\kappa(\omega,E)$ being Avila's acceleration.
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