Research Paper#Statistical Physics, Integrable Systems, Stochastic Growth Models🔬 ResearchAnalyzed: Jan 3, 2026 16:25
Stochastic Six Vertex Model and Discrete Orthogonal Polynomials
Published:Dec 27, 2025 10:13
•1 min read
•ArXiv
Analysis
This paper investigates the behavior of the stochastic six-vertex model, a model in the KPZ universality class, focusing on moderate deviation scales. It uses discrete orthogonal polynomial ensembles (dOPEs) and the Riemann-Hilbert Problem (RHP) approach to derive asymptotic estimates for multiplicative statistics, ultimately providing moderate deviation estimates for the height function in the six-vertex model. The work is significant because it addresses a less-understood aspect of KPZ models (moderate deviations) and provides sharp estimates.
Key Takeaways
- •Applies dOPEs and RHP to study the stochastic six-vertex model.
- •Focuses on moderate deviation scales, a less-understood aspect of KPZ models.
- •Provides sharp estimates for the height function in the six-vertex model.
- •Uses a novel parameter-dependent local parametrix in the RHP analysis.
Reference
“The paper derives moderate deviation estimates for the height function in both the upper and lower tail regimes, with sharp exponents and constants.”