Random walk on the self-avoiding tree.
Résumé
We consider a modified version of the biased random walk on a tree constructed from the set of finite self-avoiding walks on the hexagonal lattice, and use it to construct probability measures on infinite self-avoiding walk. Under theses probability measures, we prove that the infinite self-avoiding walks have the Russo-Seymour-Welsh property of the exploration curve of the supercritical Bernoulli percolation.
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