Tropical curves in sandpiles

Nikita Kalinin, Mikhail Shkolnikov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We study a sandpile model on the set of the lattice points in a large lattice polygon. A small perturbation ψ of the maximal stable state μ≡3 is obtained by adding extra grains at several points. It appears that the result ψo of the relaxation of ψ coincides with μ almost everywhere; the set where ψo≠μ 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.

Original languageEnglish
Pages (from-to)125-130
Number of pages6
JournalComptes Rendus Mathematique
Volume354
Issue number2
DOIs
StatePublished - 1 Feb 2016
Externally publishedYes

Keywords

  • Combinatorics
  • Mathematical physics

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