Infinite collision property for the three-dimensional uniform spanning tree

IF 0.3 Q4 MATHEMATICS, APPLIED International Journal of Mathematics for Industry Pub Date : 2023-01-20 DOI:10.1142/s2661335223500053
Satomi Watanabe
{"title":"Infinite collision property for the three-dimensional uniform spanning tree","authors":"Satomi Watanabe","doi":"10.1142/s2661335223500053","DOIUrl":null,"url":null,"abstract":"Let $\\mathcal{U}$ be the uniform spanning tree on $\\mathbb{Z}^3$, whose probability law is denoted by $\\mathbf{P}$. For $\\mathbf{P}$-a.s. realization of $\\mathcal{U}$, the recurrence of the the simple random walk on $\\mathcal{U}$ is proved in [5] and it is also demonstrated in [8] that two independent simple random walks on $\\mathcal{U}$ collide infinitely often. In this article, we will give a quantitative estimate on the number of collisions of two independent simple random walks on $\\mathcal{U}$, which provides another proof of the infinite collision property of $\\mathcal{U}$.","PeriodicalId":34218,"journal":{"name":"International Journal of Mathematics for Industry","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematics for Industry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s2661335223500053","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

Let $\mathcal{U}$ be the uniform spanning tree on $\mathbb{Z}^3$, whose probability law is denoted by $\mathbf{P}$. For $\mathbf{P}$-a.s. realization of $\mathcal{U}$, the recurrence of the the simple random walk on $\mathcal{U}$ is proved in [5] and it is also demonstrated in [8] that two independent simple random walks on $\mathcal{U}$ collide infinitely often. In this article, we will give a quantitative estimate on the number of collisions of two independent simple random walks on $\mathcal{U}$, which provides another proof of the infinite collision property of $\mathcal{U}$.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
三维均匀生成树的无限碰撞特性
设$\mathcal{U}$为$\mathbb{Z}^3$上的一致生成树,其概率律用$\mathbf{P}$表示。美元\ mathbf {P}主导者——美元。$\mathcal{U}$的实现,在[5]中证明了$\mathcal{U}$上的简单随机游动的递推性,并在[8]中证明了$\mathcal{U}$上的两个独立的简单随机游动经常无限碰撞。本文将给出$\mathcal{U}$上两个独立简单随机漫步的碰撞次数的定量估计,这再次证明了$\mathcal{U}$的无限碰撞性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
24 weeks
期刊最新文献
Optimization of Machining for the Maximal Productivity Rate of the Drilling Operations Strong Incidence Domination in Some Operations of Fuzzy Incidence Graphs and Application in Security Allocation Hybrid Technique for Multi-Dimensional Fractional Diffusion Problems Involving Caputo-Fabrizio Derivative On Fractional Pennes Bioheat Equation using Legendre Collocation Method Local Fractional Laplace Transform Iterative Method for Solving Korteweg-De Vries Equation with the Local Fractional Derivative
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1