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AIRY POINT PROCESS AT THE LIQUID-GAS BOUNDARY
Univ Grenoble Alpes, CNRS, Inst Fourier, F-38000 Grenoble, France..
Univ Durham, Dept Math Sci, Durham DH1 3LE, England..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Royal Inst Technol KTH, Dept Math, Linstedtsvagen 25, SE-10044 Stockholm, Sweden..ORCID iD: 0000-0003-2943-7006
2018 (English)In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 46, no 5, p. 2973-3013Article in journal (Refereed) Published
Abstract [en]

Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height function, we define a random measure in the two-periodic Aztec diamond designed to detect the long range correlations visible at the liquid-gas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas boundary should also be described by the Airy process.

Place, publisher, year, edition, pages
Institute of Mathematical Statistics, 2018. Vol. 46, no 5, p. 2973-3013
Keywords [en]
Domino tilings, Airy kernel point process, two-periodic Aztec diamond
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-234572DOI: 10.1214/17-AOP1244ISI: 000442612800013Scopus ID: 2-s2.0-85052125071OAI: oai:DiVA.org:kth-234572DiVA, id: diva2:1248769
Note

QC 20180917

Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2018-09-17Bibliographically approved

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