Random walk on the self-avoiding tree.

Cong Bang Huynh (1)

1 ICJ - Institut Camille Jordan

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 critical Bernoulli percolation.

Mots clés: Self-avoiding walk; random walk on tree.; Bernoulli percolation; random walk on tree

Domaines: Probabilités [math.PR]

Cong Bang Huynh. Random walk on the self-avoiding tree.. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2021, 18 (1), pp.1507. ⟨10.30757/ALEA.v18-54⟩. ⟨hal-02525438v2⟩