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Article Dans Une Revue Electronic Journal of Probability Année : 2021

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

Andrea Collevecchio
  • Fonction : Auteur
Xiaolin Zeng

Résumé

We give a simple proof for recurrence of vertex reinforced jump process on \(\mathbb{Z}^d\), under strong reinforcement. Moreover, we show how the previous result implies that linearly edge-reinforced random walk on \ \(\mathbb{Z}^d\) is {recurrent} for strong reinforcement. Finally, we prove that the \(H^{(2|2)}\) model on \(\mathbb{Z}^d\) 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.

Dates et versions

hal-02899627 , version 1 (15-07-2020)

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Andrea Collevecchio, Xiaolin Zeng. A note on recurrence of the Vertex reinforced jump process and fractional moments localization. Electronic Journal of Probability, 2021, 26, pp.63. ⟨10.1214/21-EJP609⟩. ⟨hal-02899627⟩
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