Scaling limits of random skew plane partitions

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 arbitrary slopes. Much of the limiting behavior is similar to that from [OR2]. The main difference is that when the back wall was only non-lattice slopes, the boundary of the limit shape has no singularities and is a smooth (not algebraic) curve. If a mix of lattice and non-lattice slopes are allowed, we observe the development of cusps as in [OR2], and give an analyses of the boundary. We study the fluctuations in this system at smaller scale. They are given by the beta-kernel in the bulk of the limit shape. Its asymptotic at the top of the limit shape is given by the bead process introduced in [Bou]. Near the left and right boundaries of the region we observe a new point process.