We analyze a random lozenge tiling model of a large regular hexagon, whose underlying weight structure is periodic of period $2$ in both the horizontal and vertical directions. This is a determinantal point process whose correlation kernel is expressed in terms of non-Hermitian matrix valued orthogonal polynomials. We obtain the limiting densities of the lozenges in the disordered flower-shaped region. The starting point of our analysis is a double contour formula (obtained by Duits and Kuijlaars) which involves the solution of a $4 \times 4$ Riemann-Hilbert problem. Our method generalizes the existing techniques to a model with matrix valued orthogonal polynomials.

中文翻译：

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六边形和矩阵值正交多项式的双周期菱形平铺

我们分析了一个大型正六边形的随机菱形平铺模型，其基础权重结构在水平和垂直方向上均以 $2$ 周期为周期。这是一个行列式点过程，其相关核用非厄米矩阵值的正交多项式表示。我们获得了无序花形区域中锭剂的极限密度。我们分析的起点是一个双等高公式（由 Duits 和 Kuijlaars 获得），它涉及 $4 \times 4$ Riemann-Hilbert 问题的解决方案。我们的方法将现有技术推广到具有矩阵值正交多项式的模型。