论文标题
反应扩散模型的CLT
CLT for NESS of a reaction-diffusion model
论文作者
论文摘要
我们研究了反应扩散模型的非平衡固定状态（NESS）的缩放特性。在适当的较小条件下，我们表明颗粒的密度满足了相对于NES的大量定律，并具有明确的收敛速度，并且还表明，在介质尺度上，NESS在总变异距离内通过局部平衡（产品）度量很好地近似。此外，在尺寸$ d \ leq3 $中，我们显示了颗粒下的颗粒密度的中心限制定理（CLT）。相应的高斯极限可以表示为白噪声和大量高斯自由场的独立总和，尤其是呈现宏观相关性。
We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions $d \leq3$ we show a central limit theorem (CLT) for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.
