Sandpile solitons in higher dimensions

DOI10.1007/s40598-023-00224-7arXiv2212.03717OpenAlexW4318474727MaRDI QIDQ6093959

Nikita Kalinin

Publication date: 12 September 2023

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.03717

zbMATH Keywords

cellular automatasolitonssuperharmonic functionsstringstropical geometrysandpile modeldiscrete harmonic functionssandpileshusking

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Dynamical aspects of cellular automata (37B15) Pattern formations in context of PDEs (35B36) Tropical geometry (14T99)

Cites Work

• A tropical construction of a family of real reducible curves
• Tropical curves in sandpiles
• Growth rates and explosions in sandpiles
• Sandpile solitons via smoothing of superharmonic functions
• Stability of patterns in the abelian sandpile
• The Apollonian structure of integer superharmonic matrices
• Discrete potential theory
• Deterministic Abelian Sandpile Models and Patterns

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