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In this paper we consider domino tilings of the Aztec diamond with doublyperiodic weightings. In particular a family of models which, for any $ k \in\mathbb{N} $, includes models with $ k $ smooth regions is analyzed as the sizeof the Aztec diamond tends to infinity. We use a non-intersecting pathsformulation and give a double integral formula for the correlation kernel ofthe Aztec diamond of finite size. By a classical steepest descent analysis ofthe correlation kernel we obtain the local behavior in the smooth and roughregions as the size of the Aztec diamond tends to infinity. From the mentionedlimit the macroscopic picture such as the arctic curves and in particular thenumber of smooth regions is deduced. Moreover we compute the limit of theheight function and as a consequence we confirm, in the setting of this paper,that the limit in the rough region fulfills the complex Burgers' equation, asstated by Kenyon and Okounkov.

Domino tilings of the Aztec diamond with doubly periodic weightings