ASYMPTOTICS OF UNIFORMLY RANDOM LOZENGE TILINGS OF POLYGONS. GAUSSIAN FREE FIELD

• 成果类型: Article
• 署名作者: Petrov, Leonid
• 署名单位: Northeastern University; Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP823
• 发表日期: 2015
• 页码: 1-43
• 关键词: entropy; paths

摘要

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 asymptotic analysis we use the explicit double contour integral formula for the determinantal correlation kernel of the model obtained previously in Petrov [Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes (2012) Preprint].