摘要: The tangent method has recently been devised by Colomo and Sportiello (arXiv:1605.01388 [math-ph]) as an efficient way to determine the shape of arctic curves. Largely conjectural, it tested successfully in a variety models. However no proof general geometric insight have given so far, either show its validity or allow for understanding why actually works. In this paper, we propose universal framework which accounts tangency part method, whenever formulation terms directed lattice paths is available. Our analysis shows that key factor responsible property concavity entropy (also called Lagrangean function) long random paths. We extend $q$-deformed
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