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Non-intersecting Paths, Random Tilings and Random Matrices

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arxiv math/0011250 v1 pith:KGUTS5O6 submitted 2000-11-29 math.PR math-phmath.COmath.MP

Kurt Johansson This is my paper · ORCID
classification math.PRmath-phmath.COmath.MP
keywords measuresnon-intersectingrandomtilingsmodelobtainedpathsabc-hexagon
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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 be obtained from non-intersecting Brownian motions. The derivations of the measures are based on the Karlin-McGregor or Lindstr\"om-Gessel-Viennot method. We use the measure to show some asymptotic results for the models.

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  1. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

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