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Strongly Vertex-Reinforced-Random-Walk on the complete graph
Auteur(s)
Date de parution
2012-08-31T06:07:51Z
Résumé
We study Vertex-Reinforced-Random-Walk on the complete graph with weights of the form $w(n)=n^\alpha$, with $\alpha>1$. Unlike for the Edge-Reinforced-Random-Walk, which in this case localizes a.s. on 2 sites, here we observe various phase transitions, and in particular localization on arbitrary large sets is possible, provided $\alpha$ is close enough to 1. Our proof relies on stochastic approximation techniques. At the end of the paper, we also prove a general result ensuring that any strongly reinforced VRRW on any bounded degree graph localizes a.s. on a finite subgraph.
Identifiants
Autre version
https://hal.science/hal-00724639
Type de publication
preprint
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