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2021 A note on recurrence of the Vertex reinforced jump process and fractional moments localization
Andrea Collevecchio, Xiaolin Zeng
Author Affiliations +
Electron. J. Probab. 26: 1-16 (2021). DOI: 10.1214/21-EJP609


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.

Funding Statement

A.C. was supported by ARC grant DP180100613 and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) CE140100049. X.Z. was supported by ERC starting grant 678520 and supported in part by Israel Science Foundation grant 861/15.


X. Z. want to thank R. Peled for his encouragement of writing this paper. We thank an anonymous referee for very helpful comments.


Download Citation

Andrea Collevecchio. Xiaolin Zeng. "A note on recurrence of the Vertex reinforced jump process and fractional moments localization." Electron. J. Probab. 26 1 - 16, 2021.


Received: 18 April 2020; Accepted: 24 March 2021; Published: 2021
First available in Project Euclid: 5 May 2021

Digital Object Identifier: 10.1214/21-EJP609

Primary: 60K35


Vol.26 • 2021
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