1206.5123 (Leonid Petrov)
Leonid Petrov
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 by Kenyon in 2004 (arXiv:math-ph/0405052) about tilings of regions without frozen facets of the limit shape. In our asymptotic analysis we use the explicit double contour integral formula for the determinantal correlation kernel of the model obtained in our previous work (arXiv:1202.3901 [math.PR]).
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http://arxiv.org/abs/1206.5123
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