Noncommutative geometry of random surfaces

Andrei Okounkov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 84-103.

Résumé

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.

Détail

Keywords: Dimer model, finite-difference operators, non-commutative geometry.

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