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 Z2 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 Z2, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations.
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