论图上的随机游走和弗洛伊德边界

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2021-04-28 DOI:10.4310/arkiv.2022.v60.n1.a8

P. Spanos

{"title":"论图上的随机游走和弗洛伊德边界","authors":"P. Spanos","doi":"10.4310/arkiv.2022.v60.n1.a8","DOIUrl":null,"url":null,"abstract":"We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, p(n)(v,w) ≤ Cρ, where ρ < 1 is the spectral radius, then for any Floyd function f that satisfies ∑∞ n=1 nf(n) < ∞, the Dirichlet problem with respect to the Floyd boundary is solvable.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Remarks on random walks on graphs and the Floyd boundary\",\"authors\":\"P. Spanos\",\"doi\":\"10.4310/arkiv.2022.v60.n1.a8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, p(n)(v,w) ≤ Cρ, where ρ < 1 is the spectral radius, then for any Floyd function f that satisfies ∑∞ n=1 nf(n) < ∞, the Dirichlet problem with respect to the Floyd boundary is solvable.\",\"PeriodicalId\":55569,\"journal\":{\"name\":\"Arkiv for Matematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arkiv for Matematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/arkiv.2022.v60.n1.a8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arkiv for Matematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/arkiv.2022.v60.n1.a8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们证明了对于有界图上的一致不可约随机漫步，存在一个Floyd函数，该函数使随机漫步收敛于其相应的Floyd边界。此外，如果我们加上假设p(n)(v,w)≤ρ，其中ρ < 1为谱半径，则对于任何满足∑∞n= 1nf (n) <∞的弗洛伊德函数f，关于弗洛伊德边界的Dirichlet问题是可解的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Remarks on random walks on graphs and the Floyd boundary

We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, p(n)(v,w) ≤ Cρ, where ρ < 1 is the spectral radius, then for any Floyd function f that satisfies ∑∞ n=1 nf(n) < ∞, the Dirichlet problem with respect to the Floyd boundary is solvable.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.