Dear Doron,

As I have told you earlier, I still think that our proof
of chapter 8 is slightly easier than yours : At the very
end, you need one additional summation which we do not
have to use, because our variable t appears only
for the vignette number 1. In other words, we
use one more symmetry, and linearity of
expectation, in order to avoid one
summation. You can read the
chapter 8 without reading
anything else on :

http://math.univ-lyon1.fr/~lass/articles/pub5coll.html

http://math.univ-lyon1.fr/~lass/articles/pub5collres.pdf