{"title":"泊松点云上图拉普拉斯谱的最优收敛速率","authors":"Scott Armstrong, Raghavendra Venkatraman","doi":"10.1007/s10208-025-09696-9","DOIUrl":null,"url":null,"abstract":"<p>We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.</p>","PeriodicalId":55151,"journal":{"name":"Foundations of Computational Mathematics","volume":"20 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Convergence Rates for the Spectrum of the Graph Laplacian on Poisson Point Clouds\",\"authors\":\"Scott Armstrong, Raghavendra Venkatraman\",\"doi\":\"10.1007/s10208-025-09696-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.</p>\",\"PeriodicalId\":55151,\"journal\":{\"name\":\"Foundations of Computational Mathematics\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Foundations of Computational Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10208-025-09696-9\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10208-025-09696-9","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Optimal Convergence Rates for the Spectrum of the Graph Laplacian on Poisson Point Clouds
We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.
期刊介绍：
Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer.
With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles.
The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.
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