Nonintersecting paths and the Hahn orthogonal polynomial ensemble
type: Item
instance of: scholarly article
title: Nonintersecting paths and the Hahn orthogonal polynomial ensemble
zbMATH Open document ID: 1177.60012
author: V. E. Gorin
publication date: 2009-02-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/0708.2349
review text: The paper deals with a combinatorial model of determinantal point processes in dimension \(1+1\) (one spatial and one time variable). The model depends on three positive integer parameters \(a, b,\) and \(c\) and is given by the uniform distribution on a finite set \(\Omega(a, b, c)\) of combinatorial objects. The author uses another model, where \(\Omega(a, b, c)\) is identified with an ensemble of nonintersecting polygonal paths on the plane lattice. The latter model leads to determinantal point processes (putting it otherwise, random point configurations) varying over time. The determinantal property, which is of crucial importance, means that dynamic (i.e. space-time) correlation functions of the model can be obtainet as minors of some matrix, which is called the \textit{dynamic correlation kernel}. The aim of the present paper is to compute the asymptotics of this kernel in the various limit regimes. The main result of this paper is the computation of the asymptotics of the extended Hahn kernel in the bulk limit regime.
reviewed by: N. G. Gamkrelidze
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5519876
zbMATH Keywords: tiling of a hexagon
zbMATH Keywords: plane pertition
zbMATH Keywords: determinantal process
zbMATH Keywords: orthogonal polynomial ensemble
MaRDI profile type: Publication
OpenAlex ID: W2963415950
arXiv ID: 0708.2349
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DOI: 10.1007/S10688-008-0027-1
published in: Functional Analysis and Its Applications
description: scientific article