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Fractal Self-Avoiding Walks

Abstract : For any odd integer K > 1, we define F K , a new family of self-avoiding walks (SAW) on the square lattice Z ⇥ Z, called K-fractal walks. These families have a simple and natural characterization and they seem to all have a critical exponent ⌫ for mean-square displacement in ]0.5, 1[. For small values of K at least , these families are easy to count and it is also very easy to randomly generate a K-fractal walk. In addition, lim K!1 F K is the set of all SAWs on Z ⇥ Z. We present also some variants of fractal SAWs, e.g. fractal SAWs on the d-dimensional grid Z d .
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Contributor : Pascal Préa <>
Submitted on : Saturday, January 11, 2020 - 3:11:48 PM
Last modification on : Thursday, January 16, 2020 - 1:38:42 AM
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  • HAL Id : hal-02435803, version 1



Pascal Préa. Fractal Self-Avoiding Walks. GASCom, 2012, Bordeaux, France. ⟨hal-02435803⟩



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