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

Non-intersecting paths, random tilings and random matrices