Sandpiles and unicycles on random planar maps

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.

12 pages. Section 3 is shorten

References in corpus (3)

• Basic properties of the infinite critical-FK random map
• Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone times
• Scaling limits for the critical Fortuin-Kastelyn model on a random planar map II: local estimates and empty reduced word exponent

Cited by in corpus (1)

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