In one dimension, cluster sizes grow like t^(1/(alpha+2)) for alpha > -2, and an infinite cluster forms in finite time for alpha < -2.
Procaccia, Dominik Schmid, and Daniel Sharon
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On one-dimensional Cluster cluster model
In one dimension, cluster sizes grow like t^(1/(alpha+2)) for alpha > -2, and an infinite cluster forms in finite time for alpha < -2.