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

Uwe Schwerdtfeger

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arXiv · 1101.3730

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

Uwe Schwerdtfeger

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Abstract

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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Uwe Schwerdtfeger. 2013-06-28. An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagon. https://arxiv.org/abs/1101.3730

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