COMMUNICATIONS in PROBABILITY BALLISTIC DEPOSITION ON A PLANAR STRIP

We consider ballistic diusion limited aggregation on a nite strip [0; L − 1] Z+ in Z2 for some L 2 Z+. We provide numerical bounds on the growth in the height process. 1 Model Dynamics and main result Diusion limited aggregation (DLA) is a model for crystal growth in Z2 starting from an initial seed placed at the origin. A particle is released from \innity " and performs a simple random walk until it hits a neighbor of the existing cluster where it attaches itself. Then another particle is released and the procedure repeats itself with the crystal growing at each stage. The problem is very hard to analyze and variants of the model have been studied in [5], [3], [2], [4]. For a survey and discussion see [1]. We study a simplication of this model. We consider the strip of width L with its bottom placed on the x-axis. The particles do not perform random walk but choose one of the L columns and slide down. On their slide downwards they attach themselves to the existing cluster as and when they encounter its neighborhood. This seems to be the simplest variation of the DLA model that preserves the attachment mechanism. It turns out that it is simpl