KPZ equation limit of stochastic higher spin six vertex model

DOI10.1007/s11040-019-9325-5zbMath1434.82058arXiv1905.11155OpenAlexW3099887201WikidataQ126560686 ScholiaQ126560686MaRDI QIDQ2283720

Yier Lin

Publication date: 13 January 2020

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.11155

zbMATH Keywords

Bethe ansatzKPZ equationMarkov dualitystochastic higher-spin six vertex model

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Exactly solvable models; Bethe ansatz (82B23) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs in connection with statistical mechanics (35Q82)

Related Items (12)

Convergence of ASEP to KPZ with basic coupling of the dynamics ⋮ Law of iterated logarithms and fractal properties of the KPZ equation ⋮ Orthogonal polynomial duality and unitary symmetries of multi-species ASEP \((q,\boldsymbol{\theta})\) and higher-spin vertex models via \(^*\)-bialgebra structure of higher rank quantum groups ⋮ Classification of stationary distributions for the stochastic vertex models ⋮ Lyapunov exponents of the SHE under general initial data ⋮ Strong law of large numbers for the stochastic six vertex model ⋮ The stochastic telegraph equation limit of the stochastic higher spin six vertex model ⋮ Stochastic eight-vertex model, its invariant measures and KPZ limit ⋮ On Hopf hypersurfaces of the complex quadric with recurrent Ricci tensor ⋮ A short note on Markov duality in multi-species higher spin stochastic vertex models ⋮ Stationary stochastic higher spin six vertex model and \(q\)-Whittaker measure ⋮ Spin \(q\)-Whittaker polynomials and deformed quantum Toda

Cites Work

• Unnamed Item
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• Stochastic six-vertex model
• Stochastic higher spin vertex models on the line
• A generalized asymmetric exclusion process with \(U_q(\mathfrak {sl}_2)\) stochastic duality
• A theory of regularity structures
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• KPZ reloaded
• On a family of symmetric rational functions
• Stationary stochastic higher spin six vertex model and \(q\)-Whittaker measure
• Weakly asymmetric non-simple exclusion process and the Kardar-Parisi-Zhang equation
• Integral formulas for the asymmetric simple exclusion process
• Stochastic Burgers and KPZ equations from particle systems
• \(\operatorname{ASEP}(q,j)\) converges to the KPZ equation
• Dynamical stochastic higher spin vertex models
• Current fluctuations of the stationary ASEP and six-vertex model
• The KPZ limit of ASEP with boundary
• Higher spin six vertex model and symmetric rational functions
• An algebraic construction of duality functions for the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model and its degenerations
• KPZ equation limit of higher-spin exclusion processes
• Stochastic higher spin six vertex model and \(q\)-TASEPs
• The KPZ fixed point
• Stochastic PDE limit of the six vertex model
• A stochastic telegraph equation from the six-vertex model
• Markov duality for stochastic six vertex model
• Correction to: ``Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz.
• Correction to: ``Stochastic higher spin vertex models on the line
• Weakly asymmetric bridges and the KPZ equation
• On the Yang-Baxter equation for the six-vertex model
• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• Energy solutions of KPZ are unique
• KPZ Scaling Theory and the Semi-discrete Directed Polymer Model
• Dynamic Scaling of Growing Interfaces
• On the support of solutions to the heat equation with noise
• Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian
• Open ASEP in the Weakly Asymmetric Regime
• Stochastic higher spin six vertex model and Macdonald measures
• A Multi-species ASEP $\boldsymbol{(q,\,j)}$ and $\boldsymbol{q}$-TAZRP with Stochastic Duality
• Multipoint distribution of periodic TASEP
• Stochastic telegraph equation limit for the stochastic six vertex model
• The directed landscape

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