# Sandpiles on the Square Lattice

@article{Hough2017SandpilesOT, title={Sandpiles on the Square Lattice}, author={Robert D. Hough and Daniel C. Jerison and Lionel Levine}, journal={Communications in Mathematical Physics}, year={2017}, volume={367}, pages={33-87} }

AbstractWe give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice $${\mathbb{Z}^2}$$Z2 . We also determine the asymptotic spectral gap, asymptotic mixing time, and prove a cutoff phenomenon for the recurrent state abelian sandpile model on the torus $${\left(\mathbb{Z}/m\mathbb{Z}\right)^2}$$Z/mZ2 . The techniques use analysis of the space of functions on $${\mathbb{Z}^2}$$Z2 which are harmonic modulo 1. In the course of our… CONTINUE READING

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