发表机构
IMPA; Univ. Rouen Normandie, CNRS Normandie Univ, LMRS UMR 6085; Department of Mathematics University of Arizona（巴西数学纯应用研究所; 鲁昂诺曼底大学; 亚利桑那大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究维度 $d\le 3$ 的梯度排斥过程的非平衡涨落，证明其密度涨落场在扩散尺度下收敛到线性随机偏微分方程的解。
AI 中文摘要
我们考虑离散环面 $T^d_n$（$d\le 3$）上的梯度、变速、对称排斥过程，其经验测度在扩散尺度上演化为非线性抛物方程。我们证明，从初始状态序列出发，若其相对于与初始分布相关的不均匀乘积测度的相对熵为 $o(n^{d/2})$，且密度涨落场收敛，则密度涨落场在 $L^1(0,T; H_{-r})$ 中收敛到由保守时空白噪声驱动的、具有时变系数的线性随机偏微分方程的解。
英文摘要
We consider a gradient, speed-change, symmetric exclusion process on the discrete torus $T^d_n$, $d\le 3$, whose empirical measure evolves, on the diffusive scale, according to a non-linear parabolic equation. We prove that, starting from a sequence of initial states whose relative entropy with respect to the inhomogeneous product measure associated with the initial profile is $o(n^{d/2})$, and whose density fluctuation field converges, the density fluctuation field converges, in $L^1(0,T; H_{- r})$, to the solution of a linear stochastic partial differential equation with time-dependent coefficients driven by a conservative space-time white noise.
