Displacement exponents of self-repelling walks and self-attracting walks on the pre-Sierpi\'{n}ski gasket
Vol. 12 (2005), No. 3, Page 417--443.
HATTORI, Kumiko; HATTORI, Tetsuya
Displacement exponents of self-repelling walks and self-attracting walks on the pre-Sierpi\'{n}ski gasket
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Abstract:
We construct a family of self-repelling and self-attracting walks (stochastic chains) on the (infinite) pre-{\sg}. The family continuously interpolates the simple random walk and a self-avoiding walk. The asymptotic behavior of the walks is given in terms of the displacement exponent.
Keywords: self-repelling walk, self-avoiding walk, self-attracting walk, Sierpinski gasket, displacement exponent, mean-square displacement
Mathematics Subject Classification (2000): Primary 60G17; secondary 82C41.
Mathematical Reviews Number: MR2192223
Received: 2004-08-27
