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DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS
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The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres [Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile, Potential Anal. 30(1) (2009) 1–27] as a tool to study internal diffusion limited aggregation. In this work, we investigate the shape of the divisible sandpile model on the graphical Sierpinski gasket [Formula: see text]. We show that the shape is a ball in the graph metric of [Formula: see text]. Moreover, we give an exact representation of the odometer function of the divisible sandpile.
Title: DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS
Description:
The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres [Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile, Potential Anal.
30(1) (2009) 1–27] as a tool to study internal diffusion limited aggregation.
In this work, we investigate the shape of the divisible sandpile model on the graphical Sierpinski gasket [Formula: see text].
We show that the shape is a ball in the graph metric of [Formula: see text].
Moreover, we give an exact representation of the odometer function of the divisible sandpile.
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