Asymptotics of random domino tilings of rectangular Aztec diamonds

作者：Bufetov Alexey^*; Knizel Alisa

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2018, 54(3): 1250-1290.

DOI：10.1214/17-AIHP838

• Random domino tilings
• Central limit theorem
• Moment method

We consider asymptotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a special class of examples, the explicit parametrization of the frozen boundary is given. It turns out to be an algebraic curve with very special properties. Moreover, we establish the convergence of the fluctuations of the height functions to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems.

• 出版日期2018-8
• 单位MIT