Xin Sun, David B. Wilson
Published 2015-06-29Version 1
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.
Comments: 15 pages. arXiv admin note: text overlap with arXiv:1108.2241 by other authors
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