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Scaling limits of equilibrium wetting models in (1+1)–dimension
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  • Published: 27 December 2004

Scaling limits of equilibrium wetting models in (1+1)–dimension

  • Jean–Dominique Deuschel1,
  • Giambattista Giacomin2 &
  • Lorenzo Zambotti3 

Probability Theory and Related Fields volume 132, pages 471–500 (2005)Cite this article

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  • 30 Citations

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Abstract.

We study the path properties for the δ-pinning wetting model in (1+1)–dimension. In other terms, we consider a random walk model with fairly general continuous increments conditioned to stay in the upper half plane and with a δ-measure reward for touching zero, that is the boundary of the forbidden region. It is well known that such a model displays a localization/delocalization transition, according to the size of the reward. Our focus is on getting a precise pathwise description of the system, in both the delocalized phase, that includes the critical case, and in the localized one. From this we extract the (Brownian) scaling limits of the model.

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Authors and Affiliations

  1. TU Berlin, Inst. Mathematik, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Jean–Dominique Deuschel

  2. Laboratoire de Probabilités de P 6 & 7 (CNRS U.M.R. 7599) and Université Paris 7 – Denis Diderot, U.F.R. Mathematiques, Case 7012, 2 place Jussieu, 75251, Paris cedex 05, France

    Giambattista Giacomin

  3. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Lorenzo Zambotti

Authors
  1. Jean–Dominique Deuschel
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  2. Giambattista Giacomin
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  3. Lorenzo Zambotti
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Corresponding author

Correspondence to Jean–Dominique Deuschel.

Additional information

Mathematics Subject Classification (2000): 60K35, 60F10, 82B41

J.-D. Deuschel acknowledges the financial support provided by a DFG grant.

L. Zambotti acknowledges the financial support provided by the SFB 611, University of Bonn.

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Deuschel, J., Giacomin, G. & Zambotti, L. Scaling limits of equilibrium wetting models in (1+1)–dimension. Probab. Theory Relat. Fields 132, 471–500 (2005). https://doi.org/10.1007/s00440-004-0401-8

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  • Received: 05 March 2004

  • Revised: 04 October 2004

  • Published: 27 December 2004

  • Issue Date: July 2005

  • DOI: https://doi.org/10.1007/s00440-004-0401-8

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Keywords

  • Wetting Transition
  • Critical Wetting
  • δ-Pinning Model
  • Fluctuations of Random Walks
  • Brownian scaling
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