Open Access
2018 Random surface growth and Karlin-McGregor polynomials
Theodoros Assiotis
Electron. J. Probab. 23: 1-81 (2018). DOI: 10.1214/18-EJP236


We consider consistent dynamics for non-intersecting birth and death chains, originating from dualities of stochastic coalescing flows and one dimensional orthogonal polynomials. As corollaries, we obtain unified and simple probabilistic proofs of certain key intertwining relations between multivariate Markov chains on the levels of some branching graphs. Special cases include the dynamics on the Gelfand-Tsetlin graph considered in the seminal work of Borodin and Olshanski in [10] and the ones on the BC-type graph recently studied by Cuenca in [17]. Moreover, we introduce a general inhomogeneous random growth process with a wall that includes as special cases the ones considered by Borodin and Kuan [8] and Cerenzia [15], that are related to the representation theory of classical groups and also the Jacobi growth process more recently studied by Cerenzia and Kuan [16]. Its most important feature is that, this process retains the determinantal structure of the ones studied previously and for the fully packed initial condition we are able to calculate its correlation kernel explicitly in terms of a contour integral involving orthogonal polynomials. At a certain scaling limit, at a finite distance from the wall, one obtains for a single level discrete determinantal ensembles associated to continuous orthogonal polynomials, that were recently introduced by Borodin and Olshanski in [11], and that depend on the inhomogeneities.


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Theodoros Assiotis. "Random surface growth and Karlin-McGregor polynomials." Electron. J. Probab. 23 1 - 81, 2018.


Received: 12 July 2018; Accepted: 11 October 2018; Published: 2018
First available in Project Euclid: 23 October 2018

zbMATH: 06970411
MathSciNet: MR3870449
Digital Object Identifier: 10.1214/18-EJP236

Primary: 60G

Keywords: Determinantal point processes , integrable probability , random surface growth

Vol.23 • 2018
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