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

Autor: Titus Lupu, Christophe Sabot, Pierre Tarrès
Přispěvatelé: Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), NYU–ECNU Institute of Mathematical Sciences at NYU Shanghai, NYU Shanghai, LABEX MILYON (ANR-10-LABX-0070)projet ANR MALIN (ANR-16-CE93-0003)Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich FoundationNational Science Foundation of China (NSFC), grant No. 11771293., ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2016), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2017)
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Probability Theory and Related Fields
Probability Theory and Related Fields, Springer Verlag, 2020, 177 (1-2), pp.55-90. ⟨10.1007/s00440-019-00944-y⟩
Probability Theory and Related Fields, Springer Verlag, 2019, pp.1-36. ⟨10.1007/s00440-019-00944-y⟩
ISSN: 0178-8051
1432-2064
DOI: 10.1007/s00440-019-00944-y⟩
Popis: 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. Compared to the discrete space processes, the LRM has an additional symmetry in the initial local times (initial occupation profile): changing them amounts to a deterministic change of the space and time scales.
26 pages, 1 figure. Originally called ''Scaling limit of the VRJP in dimension one and Bass-Burdzy flow''
Databáze: OpenAIRE
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