# Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field

@article{Petrov2012AsymptoticsOU, title={Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field}, author={Leonid Petrov}, journal={arXiv: Probability}, year={2012} }

We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows arbitrarily large number of sides), we show that these fluctuations are asymptotically governed by a Gaussian free (massless) field. This complements the similar result obtained in Kenyon [Comm. Math. Phys. 281 (2008) 675-709] about tilings of regions without frozen facets of the limit shape. In our…

## 71 Citations

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