Fractal Self-Avoiding Walks

International audienceFor 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