# The Height Fluctuations of an Off-Critical Dimer Model on the Square Grid

## Abstract

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In the thermodynamic limit and scaling window, these height fluctuations are shown to be non-Gaussian.

## Keywords

Dimer model Scaling window Non-Gaussian## Notes

### Acknowledgements

I would like to particularly thank Richard Kenyon for the many fruitful discussions which have led to this paper. I would also like to thank David Brydges for discussions of statistical mechanical models, Scott Sheffield for some very useful suggestions, Cédric Boutillier, Benjamin Young and Adrien Kassel for very many useful comments on this paper. Supported/Partially supported by the grant KAW 2010.0063 from the Knut and Alice Wallenberg Foundation.

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