Tropical curves in sandpiles

We study a sandpile model on the set of the lattice points in a large lattice polygon. A small perturbation Psi of the maximal stable state mu 3 is obtained by adding extra grains at several points. It appears that the result Psi degrees of the relaxation of Psi coincides with mu almost everywhere; the set where Psi degrees not equal mu is called the deviation locus. The scaling limit of the deviation locus turns out to be a distinguished tropical curve passing through the perturbation points. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.