{"title":"Benjamini-Schramm 和频谱收敛 II.非均质情况","authors":"Anton Deitmar","doi":"arxiv-2407.17264","DOIUrl":null,"url":null,"abstract":"The equivalence of spectral convergence and Benjamini-Schramm convergence is\nextended from homogeneous spaces to spaces which are compact modulo isometry\ngroup. The equivalence is proven under the condition of a uniform discreteness\nproperty. It is open, which implications hold without this condition.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Benjamini-Schramm and spectral convergence II. The non-homogeneous case\",\"authors\":\"Anton Deitmar\",\"doi\":\"arxiv-2407.17264\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The equivalence of spectral convergence and Benjamini-Schramm convergence is\\nextended from homogeneous spaces to spaces which are compact modulo isometry\\ngroup. The equivalence is proven under the condition of a uniform discreteness\\nproperty. It is open, which implications hold without this condition.\",\"PeriodicalId\":501373,\"journal\":{\"name\":\"arXiv - MATH - Spectral Theory\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-24\",\"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-2407.17264\",\"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 - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.17264","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Benjamini-Schramm and spectral convergence II. The non-homogeneous case
The equivalence of spectral convergence and Benjamini-Schramm convergence is
extended from homogeneous spaces to spaces which are compact modulo isometry
group. The equivalence is proven under the condition of a uniform discreteness
property. It is open, which implications hold without this condition.
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