This research computes asymptotic bounds on random Dehn functions in specific groups, suggesting notable differences from typical Dehn functions.
In this paper, 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.
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García-Mejía et al. (2025) studied this question.
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