Not offhand, and quite honestly, I don't have the time to research this.
It makes logical sense, both from the standpoint of how dye inks fade and
also in terms of the visual perception of fading in terms of the human
eye.
As I mentioned before, dye molecules are lost, in part, due to lack of
protection by other dye molecules. The more ink that is deposited and
that saturates into the paper (keep in mind picolitre is a volumetric
measurement) the more molecules that are deposited on top of each other,
and also the deeper into the surface the ink is likely to penetrate. Both
factors improve protection of dye molecules. Further, ink molecules are
more likely to leave from the edges of the dot, since that is where there
are less molecules of ink (the ink is more "exposed", so a larger dot will
diminish less in size relative to that surface area than a smaller dot),
reducing the perceived change in the density of the dot. Imagine that a
dot consisted of only one molecule of dye. If that one molecule, in each
case, were to "leave the paper" or oxidize and become transparent, the
whole image would disappear. But let's say each dot consisted of 10
molecules of ink, and due to the protection they afforded one another,
only 5 left the paper. The image would fade half the ink on it, but would
leave a more intact image.
There may well be research to support this somewhere on the net, (or maybe
even some to debunk it) but I can't hunt it down. If someone else has the
resources, I'm open to hear about it.
Art