For an elementary summary of a motivation of this work
(Revised version of
Uniqueness of fixed point of a two-dimensional map obtained as a generalization of the renormalization group map associated to the self-avoiding paths on gaskets in http://arxiv.org/abs/math-ph/0610007 .)
T. Hattori, T. Tsuda,
Renormalization group analysis of the self-avoiding paths
on the d-dimensional Sierpinski gaskets,
Journal of Statistical Physics 109 (2002) 39-66.
In the paper published in JSP,
rigorous mathematical proofs are replaced by brief outlines of proofs,
due to editorial decision of the journal.
The full proofs are found in the complete version linked here, which is
revised in full accordance with comments from a referee of JSP
who kindly went through the details of the proofs.
The complete version is also
in the MP_ARC preprint archive
with preprint number 02-225.
The full proof is also
in my book (in Japanese).
K. Hattori, T. Hattori, S. Kusuoka,
Self-avoiding paths on the three dimensional Sierpinski gasket,
Publications of RIMS 29 (1993) 455-509.