Asymptotics in infinite monoidal categories
Category Theory
2026-04-07 v2 Combinatorics
Representation Theory
Abstract
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories. Our focus is on monoidal categories with infinitely many indecomposable objects, with our main tools being generalized Perron-Frobenius theory alongside techniques from random walks.
Cite
@article{arxiv.2404.09513,
title = {Asymptotics in infinite monoidal categories},
author = {Abel Lacabanne and Daniel Tubbenhauer and Pedro Vaz},
journal= {arXiv preprint arXiv:2404.09513},
year = {2026}
}
Comments
21 pages, many figures, to appear in High. Struct., comments welcome