Abstract
In the paper Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201), the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arctic curve in terms of an arbitrary piecewise differentiable function that describes the defect distribution. When this distribution presents ‘freezing’ intervals, other portions of arctic curve appear and typically have a cusp. These freezing boundaries can be of two types, respectively with maximal or minimal density of defects. Our purpose here is to extend the tangent method derivation of Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201) to include these portions, hence answering the open question stated in Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Statistical Mechanics: Theory and Experiment
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
