Scaling limit of the VRJP in dimension one and Bass-Burdzy flow

Abstract : We introduce a continuous space limit of the Vertex Reinforced Jump Process (VRJP) in dimension one, which we call Linearly Reinforced Motion (LRM) on R. It is constructed out of a convergent Bass-Burdzy flow. The proof goes through the representation of the VRJP as a mixture of Markov jump processes. As a by-product this gives a representation in terms of a mixture of diffusions of the LRM and of the Bass-Burdzy flow itself. We also show that our continuous space limit can be obtained out of the Edge Reinforced Random Walk (ERRW), since the ERRW and the VRJP are known to be closely related.
Type de document :
Pré-publication, Document de travail
23 pages, 2 figures. 2018
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https://hal.archives-ouvertes.fr/hal-01745727
Contributeur : Titus Lupu <>
Soumis le : mercredi 28 mars 2018 - 14:53:44
Dernière modification le : mardi 19 mars 2019 - 01:23:26
Document(s) archivé(s) le : jeudi 13 septembre 2018 - 09:41:37

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VRJP1D14ERRW.pdf
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  • HAL Id : hal-01745727, version 1
  • ARXIV : 1803.10626

Citation

Titus Lupu, Christophe Sabot, Pierre Tarrès. Scaling limit of the VRJP in dimension one and Bass-Burdzy flow. 23 pages, 2 figures. 2018. 〈hal-01745727〉

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