Random Dehn function of groups
Group Theory
2025-08-22 v2 Metric Geometry
Probability
Abstract
In this note, we study the notion of random Dehn function and compute an asymptotic upper bound for finitely presented acylindrically hyperbolic groups whose Dehn function is at most polynomial. By showing that in these cases, if the group is not hyperbolic, then the random Dehn function is strictly smaller than the usual Dehn function we confirm Gromov's intuition albeit in a different model. In fact, we show that in these cases the random Dehn function is at most quadratic.
Cite
@article{arxiv.2411.12715,
title = {Random Dehn function of groups},
author = {Jerónimo García-Mejía and Antoine Goldsborough},
journal= {arXiv preprint arXiv:2411.12715},
year = {2025}
}
Comments
9 pages. The conclusions of Theorems A, B, and C have been strengthened. This version also includes minor corrections and improvements to the exposition following the referee's and editor's comments. Final version, accepted at Journal of Topology and Analysis