An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagon

Details An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagon An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagon

2011-01-19

arxiv.org/abs/1101.3730v1

Mathematics

Probability

20 pages, 2 figures

Scientific paper

We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in terms of discrete orthogonal polynomials. As an application we study random tilings of the half-hexagon or, equivalently, configurations of non-intersecting lattice paths above a wall, so called water melons.

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