Sandpiles and unicycles on random planar maps

Xin Sun; David B. Wilson

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arXiv · 1506.08881

Sandpiles and unicycles on random planar maps

Xin Sun·David B. Wilson

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Abstract

We consider the abelian sandpile model and the uniform spanning unicycle on random planar maps. We show that the sandpile density converges to 5/2 as the maps get large. For the spanning unicycle, we show that the length and area of the cycle converges to the hitting time and location of a simple random walk in the first quadrant. The calculations use the "hamburger-cheeseburger" construction of Fortuin--Kasteleyn random cluster configurations on random planar maps.

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BibTeX RIS

Xin Sun, David B. Wilson. 2015-08-13. Sandpiles and unicycles on random planar maps. https://arxiv.org/abs/1506.08881

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