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math-ph2026
Symmetry Emergence in Self-Organized Criticality
Ernesto Lupercio, Mikhail Shkolnikov
We describe a mechanism of affine symmetry emergence in the maximal density regime of the prototypical model of self-organized criticality when the inverse square of the mesh of th…
math-ph2025
Algebraic Limits of Sandpiles
Mikhail Shkolnikov
The paper contributes to building algebraic foundations of self-organized criticality answering a previously unsolved question about the limiting structure of the extended sandpile…
math-ph2019
Sandpile monomorphisms and limits
Moritz Lang, Mikhail Shkolnikov
We introduce a tiling problem between bounded open convex polyforms with directed and uniquely colored edges. If there exists a tiling of the polyform…