论文标题
保守的随机PDE和对称简单排除过程的波动
Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process
论文作者
论文摘要
在本文中，我们为对称简单排除过程的波动提供了一个连续模型，涉及其流体动力极限。该模型基于具有非线性，保守噪声的随机PDE的近似序列。在小噪声极限中，我们表明溶液的波动是与粒子系统的波动相同的一阶。此外，SPDES正确模拟了粒子过程中的罕见事件。我们证明，该解决方案满足零差偏差原理的速率函数等于描述对称简单排除过程与其流体动力学极限的偏差的速率函数。
In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise. In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system. Furthermore, the SPDEs correctly simulate the rare events in the particle process. We prove that the solutions satisfy a zero-noise large deviations principle with rate function equal to the rate function describing the deviations of the symmetric simple exclusion process from its hydrodynamic limit.
