Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571-609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571-609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107-142, 2009) appearing in the asymptotics at the top of the limit shape.
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机译：根据适当比例的Schur过程分布的大尺寸随机偏斜平面分区会形成极限形状。在当前工作中，我们考虑内部边界趋近具有非晶格斜率的分段线性曲线的大型随机偏斜平面分区的极限，描述了各个区域的极限形状和局部波动。此分析与Okounkov和Reshetikhin的分析相当相似（Commun Math Phys 269：571-609，2007），但是我们确实发现了一些新行为。例如，极限形状的边界现在是一条平滑的（不是代数的）曲线，而Okounkov和Reshetikhin（Commun Math Phys 269：571-609，2007）中的边界是奇异的。我们还观察到Boutillier（Ann Probab 37（1）：107-142，2009）中引入的磁珠过程出现在极限形状顶部的渐近线中。
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