Algebraic Limits of Sandpiles
Mathematical Physics
2025-09-03 v3 Combinatorics
Group Theory
math.MP
Abstract
The paper contributes to building algebraic foundations of self-organized criticality answering a previously unsolved question about the limiting structure of the extended sandpile group as well as relating it to another limit at the level of classical sandpile groups with respect to certain monomorphisms, and puts forward a concept of canonical sandpile epimorphisms, drawing an unexpected consequence about the divisibility properties of the numbers of spanning trees on rectangles.
Keywords
Cite
@article{arxiv.2506.09912,
title = {Algebraic Limits of Sandpiles},
author = {Mikhail Shkolnikov},
journal= {arXiv preprint arXiv:2506.09912},
year = {2025}
}
Comments
Several important corrections; a table is included; submitted