For finitely presented acylindrically hyperbolic groups with at most polynomial Dehn function, the random Dehn function is at most quadratic and strictly smaller than the classical Dehn function when the group is not hyperbolic.
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Random Dehn function of groups
For finitely presented acylindrically hyperbolic groups with at most polynomial Dehn function, the random Dehn function is at most quadratic and strictly smaller than the classical Dehn function when the group is not hyperbolic.