Strongly vertex-reinforced jump process on a complete graph

Olivier Raimond, Tuan Minh Nguyen

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


The aim of our work is to study vertex-reinforced jump processes with super-linear weight function w(t) = tα, for some α > 1. On any complete graph G = (V, E), we prove that there is one vertex v ∈ 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.

Original languageEnglish
Pages (from-to)1549-1568
Number of pages20
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number3
Publication statusPublished - Jul 2021


  • Non convergence to unstable equilibria
  • Nonlinear reinforcement
  • Random walks with memory
  • Stochastic approximation
  • Vertex-reinforced jump processes

Cite this