Biased 2 × 2 periodic Aztec diamond and an elliptic curve
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440_2023_Article_1195.pdf
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1.55 MB
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4bf3759906485c90350b59eb26ddcfaa
Author(s)
Borodin, Alexei
Duits, Maurice
Date Issued
February 14, 2023
Publisher
Springer Berlin Heidelberg
Citation
Borodin, Alexei and Duits, Maurice. 2023. "Biased 2 × 2 periodic Aztec diamond and an elliptic curve."
Version
Final published version
Abstract
Abstract
We study random domino tilings of the Aztec diamond with a biased
$$2 \times 2$$
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00440-023-01195-8
