The preprint of our manuscript just went online, and can be accessed under https://arxiv.org/abs/1806.10823. We also uploaded several additional videos of sandpile identity dynamics, which can be accessed in the videos section of this webpage.
Harmonic sandpile dynamics:
Moritz Lang and Mikhail Shkolnikov (2019).
Harmonic dynamics of the abelian sandpile.
Proceedings of the National Academy of Sciences (online first). DOI: 10.1073/pnas.1812015116
Sandpile monomorphisms:
Moritz Lang and Mikhail Shkolnikov (2019).
Sandpile monomorphisms and harmonic functions.
ArXiv preprint arXiv:1904.12209.
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