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Asymptotic domino statistics in the Aztec diamond
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
2015 (English)In: The Annals of Applied Probability, ISSN 1050-5164, Vol. 25, no 3, 1232-1278 p.Article in journal (Refereed) Published
Abstract [en]

We study random domino tilings of the Aztec diamond with different weights for horizontal and vertical dominoes. A domino tiling of an Aztec diamond can also be described by a particle system which is a determinantal process. We give a relation between the correlation kernel for this process and the inverse Kasteleyn matrix of the Aztec diamond. This gives a formula for the inverse Kasteleyn matrix which generalizes a result of Helfgott. As an application, we investigate the asymptotics of the process formed by the southern dominoes close to the frozen boundary. We find that at the northern boundary, the southern domino process converges to a thinned Airy point process. At the southern boundary, the process of holes of the southern domino process converges to a multiple point process that we call the thickened Airy point process. We also study the convergence of the domino process in the unfrozen region to the limiting Gibbs measure.

Place, publisher, year, edition, pages
2015. Vol. 25, no 3, 1232-1278 p.
Keyword [en]
Aztec diamond, Determinantal point process, Dimer covering, Domino tiling
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-166914DOI: 10.1214/14-AAP1021ISI: 000353527000005ScopusID: 2-s2.0-84925438268OAI: diva2:815304
Knut and Alice Wallenberg Foundation

QC 20150529

Available from: 2015-05-29 Created: 2015-05-21 Last updated: 2015-08-05Bibliographically approved

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