The Hairer--Quastel universality result in equilibrium

Hairer-Quastel universality in non-stationarity via energy solution theory

The paper addresses probabilistic aspects of the KPZ equation and stochastic Burgers equation by providing a solution theory that builds on the energy solution theory Goncalves-Jara '14, Gubinelli-Jara '13, Gubinelli-Perkowski '18, Gubinelli-Perkowski '20. The perspective we adopt is to study the stochastic Burgers equation by writing its solution as a probabilistic solution Gubinelli-Perkowski '17 plus a term that can be studied with deterministic PDE considerations. One motivation is universality of KPZ and stochastic Burgers equations for a certain class of stochastic PDE growth models, fir…

KPZ 的 Hairer–Quastel 普适性——多项式平滑机制、一般非线性与 Poisson 噪声

Hairer-Quastel universality for KPZ -- polynomial smoothing mechanisms, general nonlinearities and Poisson noise

本文证明含多项式平滑、一般非线性与 Poisson 噪声的弱非对称微观生长模型经标度后收敛到 KPZ 方程，并借助正则结构、谱间隙与 Malliavin 导数结构完成证明。

Large-scale limit of interface fluctuation models

We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of Gaussians in terms of their polynomial counterparts. This enables us to reduce the problem of a general nonlinearity with sufficient regularity to that of a polynomial.

奇异随机偏微分方程的随机模型

Random models for singular SPDEs

本文通过混沌分解和改进的费曼图收敛定理，证明了广义KPZ方程相关模型的收敛性，无需使用全部BPHZ重整化强度。

中间无序区域中有向聚合物的普适性

Universality of directed polymers in the intermediate disorder regime

本文证明了Krishnan和Quastel关于一般独立同分布权重有向聚合物在中间无序区域涨落收敛于Tracy--Widom GUE分布的猜想，对任意1/5<α<1/4成立。

Weak universality for a class of 3d stochastic reaction-diffusion models

We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic $Φ^4_3$ model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular $C^9$ is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their $L^p$ norms in terms of the graphs of the standard $Φ^4_3$ stochastic terms.