https://hal-cea.archives-ouvertes.fr/cea-01692535Di Francesco, PhilippePhilippeDi FrancescoIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueDepartment of Mathematics [Urbana] - University of Illinois at Urbana-Champaign [Urbana] - University of Illinois SystemLapa, MatthewMatthewLapaIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueArctic Curves In Path Models from The Tangent MethodHAL CCSD2018[PHYS] Physics [physics]De Laborderie, Emmanuelle2018-01-25 11:31:052022-01-04 04:41:372018-01-25 16:49:12enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-01692535/document10.1088/1751-8121/aab3c0application/pdf1Recently, Colomo and Sportiello introduced a powerful method, known as the $Tangent\ Method$, for computing the arctic curve in statistical models which have a (non-or weakly-) intersecting lattice path formulation. We apply the Tangent Method to compute arctic curves in various models: the domino tiling of the Aztec diamond for which we recover the celebrated arctic circle; a model of Dyck paths equivalent to the rhombus tiling of a half-hexagon for which we find an arctic half-ellipse; another rhombus tiling model with an arctic parabola; the vertically symmetric alternating sign matrices, where we find the same arctic curve as for unconstrained alternating sign matrices. The latter case involves lattice paths that are non-intersecting but that are allowed to have osculating contact points, for which the Tangent Method was argued to still apply. For each problem we estimate the large size asymptotics of a certain one-point function using LU decomposition of the corresponding Gessel-Viennot matrices, and a reformulation of the result amenable to asymptotic analysis.