Probability Theory and Related Fields

, Volume 123, Issue 2, pp 225–280

Non-intersecting paths, random tilings and random matrices

  • Kurt Johansson

DOI: 10.1007/s004400100187

Cite this article as:
Johansson, K. Probab. Theory Relat. Fields (2002) 123: 225. doi:10.1007/s004400100187

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Kurt Johansson
    • 1
  1. 1.Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden. e-mail: kurtj@math.kth.seSE