Non-intersecting paths, random tilings and random matrices

 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 Lindstr?m-Gessel-Viennot method. We use the measures to show some asymptotic results for the models. Received: 1 December 2000 / Revised version: 20 May 2001 / Published online: 17 May 2002