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Non-intersecting paths, random tilings and random matrices
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  • Published: June 2002

Non-intersecting paths, random tilings and random matrices

  • Kurt Johansson1 

Probability Theory and Related Fields volume 123, pages 225–280 (2002)Cite this article

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Abstract.

 We investigate certain measures induced by families of non-intersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have the same structure as the eigenvalue measures in random matrix theory like GUE, which can in fact can be obtained from non-intersecting Brownian motions. The derivations of the measures are based on the Karlin-McGregor or Lindström-Gessel-Viennot method. We use the measures to show some asymptotic results for the models.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden. e-mail: kurtj@math.kth.se, , , , , , SE

    Kurt Johansson

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  1. Kurt Johansson
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Received: 1 December 2000 / Revised version: 20 May 2001 / Published online: 17 May 2002

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Johansson, K. Non-intersecting paths, random tilings and random matrices. Probab. Theory Relat. Fields 123, 225–280 (2002). https://doi.org/10.1007/s004400100187

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  • Issue Date: June 2002

  • DOI: https://doi.org/10.1007/s004400100187

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Keywords

  • Brownian Motion
  • Growth Model
  • Matrix Theory
  • Random Matrice
  • Random Matrix
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