Biased 2 × 2 periodic Aztec diamond and an elliptic curve
Abstract We study random domino tilings of the Aztec diamond with a biased $$2 \times 2$$ 2 × 2...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2023
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| Online Access: | https://hdl.handle.net/1721.1/148125 |
| _version_ | 1811079720238841856 |
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| author | Borodin, Alexei Duits, Maurice |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Duits, Maurice |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:19:29Z |
| format | Article |
| id | mit-1721.1/148125 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:19:29Z |
| publishDate | 2023 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1481252024-01-29T21:13:10Z Biased 2 × 2 periodic Aztec diamond and an elliptic curve Borodin, Alexei Duits, Maurice Massachusetts Institute of Technology. Department of Mathematics 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. 2023-02-21T17:28:02Z 2023-02-21T17:28:02Z 2023-02-14 2023-02-19T05:37:45Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/148125 Borodin, Alexei and Duits, Maurice. 2023. "Biased 2 × 2 periodic Aztec diamond and an elliptic curve." PUBLISHER_CC en https://doi.org/10.1007/s00440-023-01195-8 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Borodin, Alexei Duits, Maurice Biased 2 × 2 periodic Aztec diamond and an elliptic curve |
| title | Biased 2 × 2 periodic Aztec diamond and an elliptic curve |
| title_full | Biased 2 × 2 periodic Aztec diamond and an elliptic curve |
| title_fullStr | Biased 2 × 2 periodic Aztec diamond and an elliptic curve |
| title_full_unstemmed | Biased 2 × 2 periodic Aztec diamond and an elliptic curve |
| title_short | Biased 2 × 2 periodic Aztec diamond and an elliptic curve |
| title_sort | biased 2 2 periodic aztec diamond and an elliptic curve |
| url | https://hdl.handle.net/1721.1/148125 |
| work_keys_str_mv | AT borodinalexei biased22periodicaztecdiamondandanellipticcurve AT duitsmaurice biased22periodicaztecdiamondandanellipticcurve |