Tangent method for the arctic curve arising from freezing boundaries

摘要: In the paper arXiv:1803.11463, authors study arctic curve arising in random tilings of some planar domains with an arbitrary distribution defects on one edge. Using tangent method they derive a parametric equation for portions terms piecewise differentiable function that describes defect distribution. When this presents "freezing" intervals, other appear and typically have cusp. These freezing boundaries can be two types, respectively maximal or minimal density defects. Our purpose here is to extend derivation arXiv:1803.11463 include these portions, hence answering open question stated arXiv:1803.11463.