空间随机网络中功率加权边长的上大偏差

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Advances in Applied Probability Pub Date : 2022-03-04 DOI:10.1017/apr.2023.10

C. Hirsch, Daniel Willhalm

{"title":"空间随机网络中功率加权边长的上大偏差","authors":"C. Hirsch, Daniel Willhalm","doi":"10.1017/apr.2023.10","DOIUrl":null,"url":null,"abstract":"\n We study the large-volume asymptotics of the sum of power-weighted edge lengths \n \n \n \n$\\sum_{e \\in E}|e|^\\alpha$\n\n \n in Poisson-based spatial random networks. In the regime \n \n \n \n$\\alpha > d$\n\n \n , we provide a set of sufficient conditions under which the upper-large-deviation asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected, and undirected variants of the k-nearest-neighbor graph, as well as suitable \n \n \n \n$\\beta$\n\n \n -skeletons.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Upper large deviations for power-weighted edge lengths in spatial random networks\",\"authors\":\"C. Hirsch, Daniel Willhalm\",\"doi\":\"10.1017/apr.2023.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n We study the large-volume asymptotics of the sum of power-weighted edge lengths \\n \\n \\n \\n$\\\\sum_{e \\\\in E}|e|^\\\\alpha$\\n\\n \\n in Poisson-based spatial random networks. In the regime \\n \\n \\n \\n$\\\\alpha > d$\\n\\n \\n , we provide a set of sufficient conditions under which the upper-large-deviation asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected, and undirected variants of the k-nearest-neighbor graph, as well as suitable \\n \\n \\n \\n$\\\\beta$\\n\\n \\n -skeletons.\",\"PeriodicalId\":53160,\"journal\":{\"name\":\"Advances in Applied Probability\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Probability\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/apr.2023.10\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/apr.2023.10","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 1

摘要

研究了基于泊松的空间随机网络中幂加权边长度和$\sum_{e \in E}|e|^\alpha$的大体积渐近性。在$\alpha > d$状态下，我们提供了一组充分条件，在这些条件下，上大偏差渐近特征为凝结现象，这意味着过量是由泊松点的可忽略部分引起的。此外，速率函数可以通过一个具体的优化问题来表示。该框架特别包含k-最近邻图的有向、双向和无向变体，以及合适的$\beta$ -骨架。

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

Upper large deviations for power-weighted edge lengths in spatial random networks

We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha > d$ , we provide a set of sufficient conditions under which the upper-large-deviation asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected, and undirected variants of the k-nearest-neighbor graph, as well as suitable $\beta$ -skeletons.

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

Advances in Applied Probability 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Advances in Applied Probability has been published by the Applied Probability Trust for over four decades, and is a companion publication to the Journal of Applied Probability. It contains mathematical and scientific papers of interest to applied probabilists, with emphasis on applications in a broad spectrum of disciplines, including the biosciences, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.