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Critical resonance in the non-intersecting lattice path model
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  • Published: 20 August 2004

Critical resonance in the non-intersecting lattice path model

  • Richard W. Kenyon1 &
  • David B. Wilson2 

Probability Theory and Related Fields volume 130, pages 289–318 (2004)Cite this article

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  • 6 Citations

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Abstract.

We study the phase transition in the honeycomb dimer model (equivalently, monotone non-intersecting lattice path model). At the critical point the system has a strong long-range dependence; in particular, periodic boundary conditions give rise to a “resonance” phenomenon, where the partition function and other properties of the system depend sensitively on the shape of the domain.

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Author information

Authors and Affiliations

  1. CNRS UMR 8628, Laboratoire de Mathématiques, Université Paris-Sud, France

    Richard W. Kenyon

  2. Microsoft Research, One Microsoft Way, Redmond, WA, USA

    David B. Wilson

Authors
  1. Richard W. Kenyon
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  2. David B. Wilson
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Corresponding author

Correspondence to David B. Wilson.

Additional information

The research leading to this article was conducted in part while the first author was visiting Microsoft.

Mathematics Subject Classification (2000): 82B20

Revised version: 7 July 2003

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Cite this article

Kenyon, R., Wilson, D. Critical resonance in the non-intersecting lattice path model. Probab. Theory Relat. Fields 130, 289–318 (2004). https://doi.org/10.1007/s00440-003-0293-z

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  • Received: 19 December 2001

  • Published: 20 August 2004

  • Issue Date: November 2004

  • DOI: https://doi.org/10.1007/s00440-003-0293-z

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Keywords

  • Boundary Condition
  • Phase Transition
  • Partition Function
  • Periodic Boundary
  • Periodic Boundary Condition
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