A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points

DOI10.1088/1751-8121/ab03ffOpenAlexW2897626858MaRDI QIDQ5052234

Philippe Di Francesco, Emmanuel Guitter

Publication date: 24 November 2022

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.07936

zbMATH Keywords

continuum limitarctic curvenon-intersecting lattice paths

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Combinatorial probability (60C05) Continuum limits in quantum field theory (81T27) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Combinatorial aspects of tessellation and tiling problems (05B45)

Related Items (12)

Arctic curves of the 6V model with partial DWBC and double Aztec rectangles ⋮ Double tangent method for two-periodic Aztec diamonds ⋮ Arctic curves of the 20V model on a triangle ⋮ Asymptotics of noncolliding q-exchangeable random walks ⋮ Enumerative combinatorics. Abstracts from the workshop held December 11--17, 2022 ⋮ Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain ⋮ Concavity analysis of the tangent method ⋮ Arctic boundaries of the ice model on three-bundle domains ⋮ Arctic curves of the twenty-vertex model with domain wall boundaries ⋮ The Arctic curve for Aztec rectangles with defects via the tangent method ⋮ Mapping TASEP Back in time ⋮ Arctic curves of the reflecting boundary six vertex and of the twenty vertex models

Cites Work

• Arctic curves of the six-vertex model on generic domains: the tangent method
• Weighted enumerations of boxed plane partitions and the inhomogeneous five-vertex model
• \(q\)-distributions on boxed plane partitions
• Planar dimers and Harnack curves
• Double-dimers, the Ising model and the hexahedron recurrence
• Binomial determinants, paths, and hook length formulae
• The shape of a typical boxed plane partition
• GUE corners limit of \(q\)-distributed lozenge tilings
• Local statistics for random domino tilings of the Aztec diamond
• Limit shapes and the complex Burgers equation
• Dimers and amoebae
• Asymptotic geometry of discrete interlaced patterns: Part I
• Arctic curves in path models from the tangent method
• Arctic curves for paths with arbitrary starting points: a tangent method approach
• A matrix model for plane partitions
• Arctic curves of the octahedron equation
• On the Vector Representations of Induced Matroids

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