Tetsuya HATTORI, Toshiro TSUDA
Asymptotic properties of self-avoiding paths on d-dimensional Seirpinski gasket from renormalization group analysis
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ABSTRACT. Notion of self avoiding fixed point, domain of attraction, and critical point are defined for self-avoiding paths on d-dimensional pre-Sierpinski gaskets, existence of which imply existence of limit distributions of scaled path lengths of `canonical ensemble', exponential growth of path numbers with respect to the length, and exponents for mean square displacement.
The definitions are written in terms of the flows of the associated renormalization-group dynamical system.
We apply the result to prove asymptotic behaviors of a certain class of self-avoiding paths on the 4-dimensional pre-Sierpinski gasket.