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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, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
2023 (English)In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 187, no 1-2, p. 259-315Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Springer Nature , 2023. Vol. 187, no 1-2, p. 259-315
National Category
Mathematics
Identifiers
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
Note

QC 20231023

Available from: 2023-10-23 Created: 2023-10-23 Last updated: 2023-10-23Bibliographically approved

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Duits, Maurice

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