The shape of large balls in highly supercritical percolation
classification
🧮 math.PR
keywords
ballsclusterlargeparameterpercolationwhenarcsasymptotically
read the original abstract
We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on $\mathbb{Z}$. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.
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