A note on recurrence of the vertex reinforced jump process and fractional moments localization

Andrea Collevecchio, Xiaolin Zeng

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


We give a simple proof for recurrence of vertex reinforced jump process on Zd, under strong reinforcement. Moreover, we show how the previous result implies that linearly edge-reinforced random walk on Zd is recurrent for strong reinforcement. Finally, we prove that the H(2|2) model on Zd localizes at strong disorder. Even though these results are well-known, we propose a unified approach, which also has the advantage to provide shorter proofs, and relies on estimating fractional moments, introduced by Aizenman and Molchanov.

Original languageEnglish
Article number63
Number of pages16
JournalElectronic Journal of Probability
Publication statusPublished - 5 May 2021


  • Localization
  • Recurrence
  • Vertex-reinforced jump process

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