Noncommutative geometry of random surfaces
Algebraic Geometry
2009-07-15 v1 Mathematical Physics
math.MP
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 in arXiv:math-ph/0507007. We also discuss various directions in which this correspondence may be generalized.
Keywords
Cite
@article{arxiv.0907.2322,
title = {Noncommutative geometry of random surfaces},
author = {Andrei Okounkov},
journal= {arXiv preprint arXiv:0907.2322},
year = {2009}
}