{"title":"The bi-dimensional Directed IDLA forest","authors":"Nicolas Chenavier, D. Coupier, A. Rousselle","doi":"10.1214/22-aap1865","DOIUrl":null,"url":null,"abstract":"We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on (cid:90) 2 with infinitely many sources that are the points of the vertical axis I ( ∞ ) = {0} × (cid:90) . Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t.the horizontal direction) random forest spanning (cid:90) 2 , based on an IDLA protocol, which is invariant in distribution w.r.t.vertical translations.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-aap1865","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on (cid:90) 2 with infinitely many sources that are the points of the vertical axis I ( ∞ ) = {0} × (cid:90) . Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t.the horizontal direction) random forest spanning (cid:90) 2 , based on an IDLA protocol, which is invariant in distribution w.r.t.vertical translations.
期刊介绍：
The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.
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