Gromov proposed an averaged version of the
Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In particular, if a nilpotent group satisfies the isoperimetric inequality
δ(l)<Cl![greek small letter alpha greek small letter alpha](http://www.sciencedirect.com/scidirimg/entities/204e.gif)
for
>2, then it satisfies the averaged isoperimetric inequality
![View the MathML source View the MathML source](http://www.sciencedirect.com/cache/MiamiImageURL/B6V1J-4PT0Y41-1-96/0?wchp=dGLbVzz-zSkzS)
. In the case of non-abelian free nilpotent groups, the bounds we give are asymptotically sharp.