Noncommutative geometry of random surfaces

Details Noncommutative geometry of random surfaces Noncommutative geometry of random surfaces

2009-07-14

arxiv.org/abs/0907.2322v1

Mathematics

Algebraic Geometry

Scientific paper

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 in arXiv:math-ph/0507007. We also discuss
various directions in which this correspondence may be generalized.

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