The stabilized single-source stochastic sandpile with p-topplings has macroscopic limit shape equal to a symmetric interval around the origin, with rescaled boundary fluctuations converging to a Gaussian.
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Limit shape of single-source stochastic sandpiles with $p$-topplings on $\mathbb{Z}$
The stabilized single-source stochastic sandpile with p-topplings has macroscopic limit shape equal to a symmetric interval around the origin, with rescaled boundary fluctuations converging to a Gaussian.