论文标题
尺寸二维的非线性随机热方程的高斯波动
Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two
论文作者
论文摘要
我们研究了空间维度二的非线性随机热方程的高斯波动。该方程是由高斯乘法噪声驱动的。噪声是白色的，在规模上$ \ varepsilon $在空间上平滑，并通过因子$ \ frac {1} {\ sqrt {\ log \ log \ varepsilon^{ - 1}}} $对数进行对数。我们证明，在居中和重新缩放之后，解决方案随机场将分布收敛到Edwards-Wilkinson限制为$ \ varepsilon \ downarrow 0 $。我们这里使用的工具是Malliavin-Stein的方法。我们还提供了此结果的功能版本。
We study the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two. The equation is driven by a Gaussian multiplicative noise. The noise is white in time, smoothed in space at scale $\varepsilon$, and tuned logarithmically by a factor $\frac{1}{\sqrt{\log \varepsilon^{-1}}}$ in its strength. We prove that, after centering and rescaling, the solution random field converges in distribution to an Edwards-Wilkinson limit as $\varepsilon \downarrow 0$. The tool we used here is the Malliavin-Stein's method. We also give a functional version of this result.
