论文标题
IDLA与无限的许多资源和指导的IDLA森林聚集在一起
IDLA aggregates with infinitely many sources and the directed IDLA forest
论文作者
论文摘要
我们研究了三种类型的内部扩散限制聚合（IDLA）模型。这些模型基于$ \ mathbf {z}^2 $上的简单随机步行，无限多个来源是垂直轴$ i（\ infty）= \ {0 \} \ times \ times \ mathbf {z} $的点。提供了各种特性，例如平稳性，混合，稳定和形状定理。我们的结果使我们能够根据IDLA协议定义一个新的定向（W.R.T.水平方向）随机森林跨越$ \ Mathbf {z}^2 $，该协议在分布W.R.T.中是不变的。垂直翻译。
We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis $I(\infty)=\{0\}\times\mathbf{Z}$. 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 $\mathbf{Z}^2$, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations.
