2024/11/19 by Jerónimo García-Mejía, García-Mejía, Jerónimo, Antoine Goldsborough +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Chemical Synthesis and Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Metric Geometry (math.MG) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2411.12715
openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.