The bi-dimensional directed IDLA forest

Nicolas Chenavier (1) , David Coupier , Arnaud Rousselle (2)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on Z 2 with infinitely many sources that are the points of the vertical axis I (∞) = {0} × 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 horizontal direction) random forest spanning Z 2 , based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations.

Mots clés: Internal Diffusion Limited Aggregation; Cluster growth; Random trees and forests; Shape theorems; Random walks

Domaines: Probabilités [math.PR]

Nicolas Chenavier, David Coupier, Arnaud Rousselle. The bi-dimensional directed IDLA forest. 2023. ⟨hal-02946661v2⟩