Fermionic structure in the Abelian sandpile and the uniform spanning tree
In this talk we consider a stochastic system of sand grains moving on a finite graph: the Abelian sandpile, a prototype of self-organized lattice model. We focus on the function that indicates whether a single grain of sand is present at a site, and explore its connections with the discrete Gaussian free field, the uniform spanning tree, and the fermionic Gaussian free field. Based on joint works with L. Chiarini (Durham), R. S. Hazra (Leiden), A. Rapoport and W. Ruszel (Utrecht).
Area: IS12 - Random surfaces (Alessandra Cipriani)
Keywords: Scaling limit, fermionic Gaussian free field, Abelian sandpile, uniform spanning tree