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May 2021 Random interlacements for vertex-reinforced jump processes
Franz Merkl, Silke W. W. Rolles, Pierre Tarrès
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Ann. Inst. H. Poincaré Probab. Statist. 57(2): 1058-1080 (May 2021). DOI: 10.1214/20-AIHP1107

Abstract

We introduce random interlacements for transient vertex-reinforced jump processes on a general graph G. Using increasing finite subgraphs Gn of G with wired boundary conditions, we show convergence of the vertex-reinforced jump process on Gn observed in a finite window to the random interlacement observed in the same window.

Nous introduisons les entrelacs aléatoires pour le processus de sauts renforcé par sommets sur un graphe général G. A l’aide d’une suite croissante de sous-graphes Gn de G avec condition aux limites de Dirichlet, nous montrons la convergence du processus de sauts renforcé par sommets sur Gn observé sur une fenêtre finie vers l’entrelacs aléatoire observé sur la même fenêtre.

Acknowledgements

This work is supported by National Science Foundation of China (NSFC), grant No. 11771293, by the Agence Nationale de la Recherche (ANR) in France, project MALIN, No. ANR-16-CE93-0003 and by the Australian Research Council (ARC) grant DP180100613.

Citation

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Franz Merkl. Silke W. W. Rolles. Pierre Tarrès. "Random interlacements for vertex-reinforced jump processes." Ann. Inst. H. Poincaré Probab. Statist. 57 (2) 1058 - 1080, May 2021. https://doi.org/10.1214/20-AIHP1107

Information

Received: 19 March 2019; Revised: 5 February 2020; Accepted: 22 September 2020; Published: May 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AIHP1107

Subjects:
Primary: 60K35
Secondary: 60J27, 60K37

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

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Vol.57 • No. 2 • May 2021
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