{"title":"双向定向IDLA森林","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":"{\"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}","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}
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
