{"title":"Stable trees as mixings of inhomogeneous continuum random trees","authors":"Minmin Wang","doi":"10.1016/j.spa.2024.104404","DOIUrl":null,"url":null,"abstract":"<div><p>It has been claimed in Aldous et al. (2004) that all Lévy trees are mixings of inhomogeneous continuum random trees. We give a rigorous proof of this claim in the case of a stable branching mechanism, relying on a new procedure for recovering the tree distance from the graphical spanning trees that works simultaneously for stable trees and inhomogeneous continuum random trees.</p></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"175 ","pages":"Article 104404"},"PeriodicalIF":1.1000,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304414924001108/pdfft?md5=d3e1a880f6ad38447d891d0fc7b9d90e&pid=1-s2.0-S0304414924001108-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Processes and their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304414924001108","RegionNum":2,"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: 0
Abstract
It has been claimed in Aldous et al. (2004) that all Lévy trees are mixings of inhomogeneous continuum random trees. We give a rigorous proof of this claim in the case of a stable branching mechanism, relying on a new procedure for recovering the tree distance from the graphical spanning trees that works simultaneously for stable trees and inhomogeneous continuum random trees.
期刊介绍：
Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests.
Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.
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