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 Z2 with infinitely many sources that are the points of the vertical axis I (infinity) = {0}x Z. Various properties are provided, such as stationarity, mixing, stabiliz...

Full description

Saved in:

Bibliographic Details
Published in:	The Annals of applied probability Vol. 33; no. 3; pp. 2247 - 2290
Main Authors:	Coupier, David, Rousselle, Arnaud, Chenavier, Nicolas
Format:	Journal Article
Language:	English
Published:	Institute of Mathematical Statistics (IMS) 01-06-2023
Subjects:	Mathematics Probability Statistics random walks cluster growth Internal diffusion limited aggregation shape theorems random trees and forests
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We investigate three types of internal diffusion limited aggregation (IDLA) models. These models are based on simple random walks on Z2 with infinitely many sources that are the points of the vertical axis I (infinity) = {0}x Z. 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 hor-izontal direction) random forest spanning Z2, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations.
ISSN:	1050-5164 2168-8737
DOI:	10.1214/22-AAP1865