  The growth of the second moments of the solutions of fast diffusion equations
is asymptotically governed by the behavior of self-similar solutions. However,
at next order, there is a correction term which amounts to a delay depending on
the nonlinearity and on a distance of the initial data to the set of
self-similar Barenblatt solutions. This distance can be measured in terms of a
relative entropy to the best matching Barenblatt profile. This best matching
Barenblatt function determines a scale. In new variables based on this scale,
which are given by a self-similar change of variables if and only if the
initial datum is one of the Barenblatt profiles, the typical scale is monotone
and has a li
