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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 1, Pages 84–103
DOI: https://doi.org/10.4213/faa4181 (Mi faa4181) 		 
Noncommutative geometry of random surfaces

Andrei Okounkov

Columbia University, New York, USA
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DOI: https://doi.org/10.4213/faa4181
Abstract: We associate a noncommutative curve to a periodic, bipartite, planar dimer model with polygonal boundary. It determines the inverse Kasteleyn matrix and hence all correlations. It may be seen as a quantization of the limit shape construction of Kenyon and the author. We also discuss various directions in which this correspondence may be generalized.
Keywords: Dimer model, finite-difference operators, non-commutative geometry.
Funding agency
The author thanks the Simons Foundation for supporting his research.
Received: 25.11.2023
Revised: 26.11.2023
Accepted: 26.11.2023
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 1, Pages 65–79
DOI: https://doi.org/10.1134/S0016266324010064
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Andrei Okounkov, “Noncommutative geometry of random surfaces”, Funktsional. Anal. i Prilozhen., 58:1 (2024), 84–103; Funct. Anal. Appl., 58:1 (2024), 65–79
Citation in format AMSBIB
\Bibitem{Oko24}
\by Andrei Okounkov
\paper Noncommutative geometry of random surfaces
\jour Funktsional. Anal. i Prilozhen.
\yr 2024
\vol 58
\issue 1
\pages 84--103
\mathnet{http://mi.mathnet.ru/faa4181}
\crossref{https://doi.org/10.4213/faa4181}
\transl
\jour Funct. Anal. Appl.
\yr 2024
\vol 58
\issue 1
\pages 65--79
\crossref{https://doi.org/10.1134/S0016266324010064}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85193462960}
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