 02225 Tetsuya HATTORI, Toshiro TSUDA
 Renormalization group analysis of the selfavoiding paths on the ddimensional Sierpinski gaskets
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May 13, 02

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Abstract. Notion of the renormalization group dynamical system, the selfavoiding fixed point and the critical trajectory are mathematically defined for the set of selfavoiding walks on the ddimensional preSierpinski gaskets (nsimplex lattices), such that their existence imply the asymptotic behaviors of the selfavoiding walks, such as the existence of the limit distributions of the scaled path lengths of `canonical ensemble', the connectivity constant (exponential growth of path numbers with respect to the length), and the exponent for mean square displacement.
We apply the so defined framework to prove these asymptotic behaviors of the restricted selfavoiding walks on the 4dimensional preSierpinski gasket.
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