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math.AP2026

On the Smoluchowski-Kramers approximation for the hyperbolic linear sigma model and its mean-field limit

Alexander Czernik, Ruoyuan Liu, Shao Liu

We study the hyperbolic linear sigma model, i.e. a system of interacting stochastic damped nonlinear wave equations (SdNLW) with coupled cubic nonlinearities, posed on t…

math.AP2026

Hyperbolic linear sigma model and its mean-field limit

Ruoyuan Liu, Shao Liu, Tadahiro Oh

We study large limits of the hyperbolic linear sigma model () on the two-dimensional torus , namely, a system of interacting stochastic d…

math.AP2026

Large torus limit of global dynamics of the two-dimensional dispersive Anderson model

Ruoyuan Liu, Nikolay Tzvetkov

We continue the study of the two-dimensional dispersive Anderson model (DAM), i.e. the nonlinear Schrödinger equation with multiplicative spatial white noise. For this model, glob…

math.AP2024

Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic -model

Ruoyuan Liu, Nikolay Tzvetkov, Yuzhao Wang

We study the fractional -measure (with order ) and the dynamical problem of its canonical stochastic quantization: the three-dimensional stochastic damped fractional…

math.AP2024

Global well-posedness of the energy-critical stochastic nonlinear wave equations

Enguerrand Brun, Guopeng Li, Ruoyuan Liu

We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on and $\mathbb{T}…