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arXiv · 1810.06905

Strongly vertex-reinforced jump process on a complete graph

Olivier Raimond·Tuan-Minh Nguyen
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Abstract

The aim of our work is to study vertex-reinforced jump processes with super-linear weight function $w(t) = t^α$ , for some $α>1$. 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.

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Olivier Raimond, Tuan-Minh Nguyen. 2021-03-18. Strongly vertex-reinforced jump process on a complete graph. https://doi.org/10.1214/20-aihp1115

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