Strongly vertex-reinforced jump process on a complete graph

Abstract

The aim of our work is to study vertex-reinforced jump processes with super-linear weight function $w(t)=t^{\alpha }$ , for some $\alpha >1$. On any complete graph $G=(V,E)$, we prove that there is one vertex $v\in V$ such that the total time spent at $v$ almost surely tends to infinity while the total time spent at the remaining vertices is bounded.

26 pages

References in corpus (5)

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Cited by in corpus (2)

• A note on recurrence of the Vertex reinforced jump process and fractional moments localization
• Vertex-reinforced jump process on the integers with nonlinear reinforcement