Stochastic higher spin six vertex model and Macdonald measures

DOI10.1063/1.5000046zbMath1382.82029arXiv1608.01553OpenAlexW2504041815MaRDI QIDQ4607698

Alexei Borodin

Publication date: 14 March 2018

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

Full work available at URL: https://arxiv.org/abs/1608.01553

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Exactly solvable dynamic models in time-dependent statistical mechanics (82C23)

Related Items

The ASEP and determinantal point processes ⋮ Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process ⋮ Hall-Littlewood RSK field ⋮ Nonsymmetric Macdonald polynomials via integrable vertex models ⋮ Stochastic symplectic ice ⋮ KPZ and Airy limits of Hall-Littlewood random plane partitions ⋮ Moments match between the KPZ equation and the Airy point process ⋮ Dynamical stochastic higher spin vertex models ⋮ Symmetric elliptic functions, IRF models, and dynamic exclusion processes ⋮ Lower tail of the KPZ equation ⋮ Observables of coloured stochastic vertex models and their polymer limits ⋮ Limit shapes and local statistics for the stochastic six-vertex model ⋮ Fluctuations for stationary \(q\)-TASEP ⋮ A stochastic telegraph equation from the six-vertex model ⋮ The lower tail of \(q\)-pushTASEP ⋮ Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation ⋮ New approach to KPZ models through free fermions at positive temperature ⋮ HALF-SPACE MACDONALD PROCESSES ⋮ GOE fluctuations for the maximum of the top path in alternating sign matrices ⋮ PushTASEP in inhomogeneous space ⋮ Two-point convergence of the stochastic six-vertex model to the Airy process ⋮ Refined Littlewood identity for spin Hall-Littlewood symmetric rational functions ⋮ The ASEP speed process ⋮ The KPZ limit of ASEP with boundary ⋮ \( \text{GUE}\times \text{GUE}\) limit law at hard shocks in ASEP ⋮ Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles ⋮ Preface: Introduction to special issue: In memory of Ludwig Faddeev ⋮ KPZ equation limit of stochastic higher spin six vertex model ⋮ Color-position symmetry in interacting particle systems ⋮ The stochastic telegraph equation limit of the stochastic higher spin six vertex model ⋮ Free field approach to the Macdonald process ⋮ Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations ⋮ Refined Cauchy identity for spin Hall-Littlewood symmetric rational functions ⋮ The \(q\)-TASEP with a random initial condition ⋮ YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic six-vertex model
• Stochastic higher spin vertex models on the line
• Determinantal structures in the O'Connell-Yor directed random polymer model
• Moments match between the KPZ equation and the Airy point process
• Anisotropic growth of random surfaces in \({2+1}\) dimensions
• Directed polymers and the quantum Toda lattice
• A new generalisation of Macdonald polynomials
• Random skew plane partitions and the Pearcey process
• A Fredholm determinant representation in ASEP
• Asymptotics in ASEP with step initial condition
• Level-spacing distributions and the Airy kernel
• Distributions on partitions, point processes, and the hypergeometric kernel
• KPZ and Airy limits of Hall-Littlewood random plane partitions
• Higher spin six vertex model and symmetric rational functions
• Shape fluctuations and random matrices
• The ASEP and determinantal point processes
• Phase transitions in the ASEP and stochastic six-vertex model
• Integrable probability: from representation theory to MacDonald processes
• Macdonald processes
• The arctic circle boundary and the Airy process
• Representations of the Infinite Symmetric Group
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian
• Lectures on integrable probability
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• Asymptotics of Plancherel measures for symmetric groups
• Discrete orthogonal polynomial ensembles and the Plancherel measure
• Infinite wedge and random partitions