A note on the quicksort asymptotics

In a recent paper, Bindjeme and Fill obtained a surprisingly easy exact formula for the L2-distance of the (normalized) number of comparisons of Quicksort under the uniform model to its limit. Shortly afterwards, Neininger proved a central limit theorem for the error. As a consequence, he obtained the asymptotics of the L3-distance. In this short note, we use the moment transfer approach to re-prove Neininger’s result. As a consequence, we obtain the asymptotics of the Lp-distance for all p ≥ 1.