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An Invariance Principle to Ferrari-Spohn Diffusions

Ioffe, Dmitry ; Shlosman, Senya ; Velenik, Yvan

In: Communications in Mathematical Physics, 2015, vol. 336, no. 2, p. 905-932

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    Titre
    • An Invariance Principle to Ferrari-Spohn Diffusions
    Auteur
    • Ioffe, Dmitry. William Davidson Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, 32000, Technion City, Haifa, Israel
    • Shlosman, Senya. Aix Marseille Université, Université de Toulon, CNRS, CPT UMR 7332, 13288, Marseille, France
    • Velenik, Yvan. Section de Mathématiques, Université de Genève, 2-4, rue du Lièvre, Case postale 64, 1211, Geneva, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Communications in Mathematical Physics, 2015, vol. 336, no. 2, p. 905-932. Springer Berlin Heidelberg
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:330944
    Summary
    We prove an invariance principle for a class of tilted 1+1-dimensional SOS models or, equivalently, for a class of tilted random walk bridges in $${\mathbb{Z}_+}$$ Z + . The limiting objects are stationary reversible ergodic diffusions with drifts given by the logarithmic derivatives of the ground states of associated singular Sturm-Liouville operators. In the case of a linear area tilt, we recover the Ferrari-Spohn diffusion with log-Airy drift, which was derived in Ferrari and Spohn (Ann Probab 33(4):1302—1325, 2005) in the context of Brownian motions conditioned to stay above circular and parabolic barriers.