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Tropical curves in sandpiles. / Kalinin, Nikita; Shkolnikov, Mikhail.

In: Comptes Rendus Mathematique, Vol. 354, No. 2, 01.02.2016, p. 125-130.

Research output: Contribution to journal › Article › peer-review

Harvard

Kalinin, N & Shkolnikov, M 2016, 'Tropical curves in sandpiles', Comptes Rendus Mathematique, vol. 354, no. 2, pp. 125-130. https://doi.org/10.1016/j.crma.2015.11.003

APA

Kalinin, N., & Shkolnikov, M. (2016). Tropical curves in sandpiles. Comptes Rendus Mathematique, 354(2), 125-130. https://doi.org/10.1016/j.crma.2015.11.003

Vancouver

Kalinin N, Shkolnikov M. Tropical curves in sandpiles. Comptes Rendus Mathematique. 2016 Feb 1;354(2):125-130. https://doi.org/10.1016/j.crma.2015.11.003

Author

Kalinin, Nikita ; Shkolnikov, Mikhail. / Tropical curves in sandpiles. In: Comptes Rendus Mathematique. 2016 ; Vol. 354, No. 2. pp. 125-130.

BibTeX

@article{2d843f8694054cee8169728cda77b9fb,
title = "Tropical curves in sandpiles",
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.",
keywords = "Combinatorics, Mathematical physics",
author = "Nikita Kalinin and Mikhail Shkolnikov",
year = "2016",
month = feb,
day = "1",
doi = "10.1016/j.crma.2015.11.003",
language = "English",
volume = "354",
pages = "125--130",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Tropical curves in sandpiles

AU - Kalinin, Nikita

AU - Shkolnikov, Mikhail

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

KW - Combinatorics

KW - Mathematical physics

UR - http://www.scopus.com/inward/record.url?scp=84956918156&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2015.11.003

DO - 10.1016/j.crma.2015.11.003

M3 - Article

AN - SCOPUS:84956918156

VL - 354

SP - 125

EP - 130

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 2

ER -

ID: 49793752