# Strongly reinforced Vertex-Reinforced-Random-Walk on complete graphs

Stochastic Analysis Seminar Series

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.

This is a joint work with Michel Benaïm and Bruno Schapira.

 Location: AHL Lecture Theatre, OMI, Eagle House Speaker(s): Oliver Raimond (Paris) Date: Monday, October 22, 2012 - 14:15 to 15:15