Tropical curves in sandpiles

DOI10.1016/j.crma.2015.11.003zbMath1366.05127arXiv1509.02303OpenAlexW2204560070MaRDI QIDQ512332

Mikhail Shkolnikov, Nikita Kalinin

Publication date: 24 February 2017

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02303

zbMATH Keywords

combinatoricsmathematical physics

Mathematics Subject Classification ID

Related Items (10)

Laplacian growth and sandpiles on the Sierpiński gasket: limit shape universality and exact solutions ⋮ Sandpile monomorphisms and limits ⋮ Introduction to tropical series and wave dynamic on them ⋮ Sandpile solitons in higher dimensions ⋮ Sandpile solitons via smoothing of superharmonic functions ⋮ The number \(\pi \) and a summation by \(\mathrm{SL}(2,\mathbb {Z})\) ⋮ The spectrum of the abelian sandpile model ⋮ Stability of patterns in the abelian sandpile ⋮ Sandpiles on the heptagonal tiling ⋮ Examples of tropical-to-Lagrangian correspondence

Cites Work

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• Growth rates and explosions in sandpiles
• On the identity of the sandpile group
• Convergence of the abelian sandpile
• The number of vertices of a tropical curve is bounded by its area
• Self-organized critical state of sandpile automaton models
• Enumerative tropical algebraic geometry in ℝ²
• Brief introduction to tropical geometry

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