Mikhail Shkolnikov
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Relaxation in one-dimensional tropical sandpile
cm:10483 -
Communications in Mathematics,
September 26, 2023,
Volume 31 (2023), Issue 3 (Special issue: in memory of Sergei Duzhin)
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https://doi.org/10.46298/cm.10483Relaxation in one-dimensional tropical sandpileArticle
Authors: Mikhail Shkolnikov
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Mikhail Shkolnikov
A relaxation in the tropical sandpile model is a process of deforming a tropical hypersurface towards a finite collection of points. We show that, in the one-dimensional case, a relaxation terminates after a finite number of steps. We present experimental evidence suggesting that the number of such steps obeys a power law.
Volume: Volume 31 (2023), Issue 3 (Special issue: in memory of Sergei Duzhin)
Published on: September 26, 2023
Accepted on: September 9, 2023
Submitted on: December 14, 2022
Keywords: Mathematics - Combinatorics, Nonlinear Sciences - Adaptation and Self-Organizing Systems