双向定向IDLA森林

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2023-06-01 DOI:10.1214/22-aap1865

Nicolas Chenavier, D. Coupier, A. Rousselle

{"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}

引用次数: 0

摘要

我们研究了三种类型的内部扩散有限聚集(IDLA)模型。这些模型基于(cid:90) 2上的简单随机漫步，具有无限多个源，这些源是垂直轴I(∞)= {0}× (cid:90)的点。提供了各种性质，如平稳性、混合性、稳定性和形状定理。我们的结果允许我们基于IDLA协议定义一个新的有向(水平方向)随机森林(cid:90) 2，该协议在垂直方向上的分布是不变的。

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

The bi-dimensional Directed IDLA forest

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.

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

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

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.