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2016 Sandpiles and unicycles on random planar maps
Xin Sun, David B. Wilson
Electron. Commun. Probab. 21(none): 1-12 (2016). DOI: 10.1214/16-ECP4477

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 exit location and exit time 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.

Citation

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Xin Sun. David B. Wilson. "Sandpiles and unicycles on random planar maps." Electron. Commun. Probab. 21 1 - 12, 2016. https://doi.org/10.1214/16-ECP4477

Information

Received: 12 August 2015; Accepted: 25 July 2016; Published: 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1348.82025
MathSciNet: MR3548769
Digital Object Identifier: 10.1214/16-ECP4477

Subjects:
Primary: 05C05, 60C05, 82B20

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