{"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}
引用次数: 1
Abstract
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.
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.
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