Dimers on rail yard graphs

DOI10.4171/AIHPD/46zbMath1391.82008arXiv1504.05176OpenAlexW3102146450MaRDI QIDQ679659

Sylvie Corteel, Guillaume Chapuy, Sanjay Ramassamy, Cédric Boutillier, Jérémie Bouttier

Publication date: 19 January 2018

Published in: Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05176

zbMATH Keywords

vertex operatorsplane partitionsAztec diamonddeterminantal processesSchur processfree fermionsdimer models

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Domino statistics of the two-periodic Aztec diamond ⋮ Asymptotics of random domino tilings of rectangular Aztec diamonds ⋮ The free boundary Schur process and applications. I ⋮ Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices ⋮ Arctic curves of the six-vertex model on generic domains: the tangent method ⋮ From Aztec diamonds to pyramids: Steep tilings ⋮ Asymptotics of pure dimer coverings on rail yard graphs ⋮ Discrete dynamics in cluster integrable systems from geometric \(R\)-matrix transformations ⋮ The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions ⋮ Interface fluctuations associated with split Fermi seas ⋮ Free fermion six vertex model: symmetric functions and random domino tilings ⋮ Arctic curve of the free-fermion six-vertex model in an L-shaped domain ⋮ Arctic boundaries of the ice model on three-bundle domains ⋮ The free boundary Schur process and applications ⋮ Airy point process at the liquid-gas boundary ⋮ Periodic Pólya urns, the density method and asymptotics of Young tableaux ⋮ Fourier transform on high-dimensional unitary groups with applications to random tilings

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