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Biased 2 × 2 periodic Aztec diamond and an elliptic curve
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139, USA, 77 Massachusetts Ave..
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).ORCID-id: 0000-0002-7598-4521
2023 (engelsk)Inngår i: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 187, nr 1-2, s. 259-315Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We study random domino tilings of the Aztec diamond with a biased 2 × 2 periodic weight function and associate a linear flow on an elliptic curve to this model. Our main result is a double integral formula for the correlation kernel, in which the integrand is expressed in terms of this flow. For special choices of parameters the flow is periodic, and this allows us to perform a saddle point analysis for the correlation kernel. In these cases we compute the local correlations in the smooth disordered (or gaseous) region. The special example in which the flow has period six is worked out in more detail, and we show that in that case the boundary of the rough disordered region is an algebraic curve of degree eight.

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Springer Nature , 2023. Vol. 187, nr 1-2, s. 259-315
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URN: urn:nbn:se:kth:diva-338417DOI: 10.1007/s00440-023-01195-8ISI: 000933433200001PubMedID: 37655050Scopus ID: 2-s2.0-85147992049OAI: oai:DiVA.org:kth-338417DiVA, id: diva2:1806638
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QC 20231023

Tilgjengelig fra: 2023-10-23 Laget: 2023-10-23 Sist oppdatert: 2023-10-23bibliografisk kontrollert

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