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

2011/01/19 by Uwe Schwerdtfeger, Schwerdtfeger, Uwe
Mathematics · #60K35 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.1101.3730

25 pages, 2 figures, improved exposition, corrected typos

arxiv created 2013/06/28 · arxiv updated 2015/03/17

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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