24 citations · 108 across the 21 of their papers we have counts for
5 papers · 1 filter
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…
Limits of Equi-Affine Equi-Distant Loci of Planar Convex Domains with Two Non-Parallel Asymptotes
Nikita Kalinin, Mikhail Shkolnikov
In this note, we introduce equi-affine invariants by averaging over the space of tropical structures of fixed covolume. Applied to the tropical distance series, this construction p…
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…
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…
Harmonic dynamics of the Abelian sandpile
Moritz Lang, Mikhail Shkolnikov
The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group i…