Search:
Match:
2 results
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.
Reference

“The paper derives moderate deviation estimates for the height function in both the upper and lower tail regimes, with sharp exponents and constants.”

PermalinkArXiv
Research Paper#Nonlinear Schrödinger Equation, Manakov System, Asymptotics🔬 ResearchAnalyzed: Jan 3, 2026 16:37

Long-Time Asymptotics for Defocusing Manakov System

Published:Dec 26, 2025 03:03
1 min read
ArXiv

Analysis

This paper addresses a significant open problem in the field of nonlinear Schrödinger equations, specifically the long-time behavior of the defocusing Manakov system under nonzero background conditions. The authors provide a detailed proof for the asymptotic formula, employing a Riemann-Hilbert problem and the Deift-Zhou steepest descent analysis. A key contribution is the identification and explicit expression of a dispersive correction term not present in the scalar case.
Reference

“The leading order of the solution takes the form of a modulated multisoliton. Apart from the error term, we also discover that the defocusing Manakov system has a dispersive correction term of order $t^{-1/2}$, but this term does not exist in the scalar case...”

PermalinkArXiv