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Preprints, Working Papers, ... Year : 2023

The bi-dimensional directed IDLA forest

Abstract

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.
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Dates and versions

hal-02946661 , version 1 (23-09-2020)
hal-02946661 , version 2 (05-05-2023)

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