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Non-Gaussian surface pinned by a weak potential
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  • Published: March 2000

Non-Gaussian surface pinned by a weak potential

  • J.-D. Deuschel1 &
  • Y. Velenik<!-ID="*"Supported by DFG grant De 663/2-1.-->2 

Probability Theory and Related Fields volume 116, pages 359–377 (2000)Cite this article

Abstract.

We consider a model of a two-dimensional interface of the (continuous) SOS type, with finite-range, strictly convex interactions. We prove that, under an arbitrarily weak pinning potential, the interface is localized. We consider the cases of both square well and δ potentials. Our results extend and generalize previous results for the case of nearest-neighbours Gaussian interactions in [7] and [11]. We also obtain the tail behaviour of the height distribution, which is not Gaussian.

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Authors and Affiliations

  1. Fachbereich Mathematik, Sekr. MA 7-4, TU-Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany. e-mail address: deuschel@math.tu-berlin.de, , , , , , DE

    J.-D. Deuschel

  2. Fachbereich Mathematik, Sekr. MA 7-4, TU-Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany. e-mail address: velenik@math.tu-berlin.de, , , , , , DE

    Y. Velenik<!-ID="*"Supported by DFG grant De 663/2-1.-->

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  1. J.-D. Deuschel
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  2. Y. Velenik<!-ID="*"Supported by DFG grant De 663/2-1.-->
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Received: 3 November 1998 / Revised version: 14 June 1999

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Cite this article

Deuschel, JD., Velenik<!-ID="*"Supported by DFG grant De 663/2-1.-->, Y. Non-Gaussian surface pinned by a weak potential. Probab Theory Relat Fields 116, 359–377 (2000). https://doi.org/10.1007/s004400070004

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  • Issue Date: March 2000

  • DOI: https://doi.org/10.1007/s004400070004

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Keywords

  • Height Distribution
  • Weak Potential
  • Tail Behaviour
  • Gaussian Interaction
  • Convex Interaction
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