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

Understand

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.