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The two-periodic Aztec diamond and matrix valued orthogonal polynomials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200 B, B-3001 Leuven, Belgium..
2021 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 23, no 4, p. 1029-1131Article in journal (Refereed) Published
Abstract [en]

We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices. In a more general framework we express the correlation kernel for the underlying determinantal point process as a double contour integral that contains the reproducing kernel of matrix valued orthogonal polynomials. We use the Riemann-Hilbert problem to simplify this formula for the case of the two-periodic Aztec diamond. In the large size limit we recover the three phases of the model known as solid, liquid and gas. We describe the fine asymptotics for the gas phase and at the cusp points of the liquid-gas boundary, thereby complementing and extending results of Chhita and Johansson.

Place, publisher, year, edition, pages
European Mathematical Society - EMS - Publishing House GmbH , 2021. Vol. 23, no 4, p. 1029-1131
Keywords [en]
Aztec diamond, random tilings, matrix valued orthogonal polynomials, Riemann-Hilbert problems
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-292604DOI: 10.4171/JEMS/1029ISI: 000627870800002Scopus ID: 2-s2.0-85103572191OAI: oai:DiVA.org:kth-292604DiVA, id: diva2:1543447
Note

QC 20210412

Available from: 2021-04-12 Created: 2021-04-12 Last updated: 2022-06-25Bibliographically approved

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Duits, Maurice

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
  • html
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