Geodesic
Noncommutative geometry of random surfaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 84-103

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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. 
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Andrei Okounkov. Noncommutative geometry of random surfaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 84-103. http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a5/