Mathematics
5 years ago

New method creates self-avoiding walks with unique path properties.

Discrete and Continuous Dynamical Systems - S
A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpiński gasket
Kumiko Hattori, Noriaki Ogo, Takafumi Otsuka

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The article introduces a new family of self-avoiding walks on the Sierpiński gasket by using a method called 'erasing-larger-loops-first'. This method connects the loop-erased random walk and a self-avoiding walk with similar behaviors. The researchers prove the existence of a scaling limit and find that the path properties vary continuously with a parameter. The limit process is self-avoiding and has a path dimension greater than 1.