论文标题
紧凑的riemannian歧管上对称排除过程的平衡波动
Equilibrium fluctuations for the Symmetric Exclusion Process on a compact Riemannian manifold
论文作者
论文摘要
如Van Ginkel和Redig（2020年）所引入的，我们考虑了紧凑的Riemannian歧管上的对称排除过程。在那里，表明流体动力极限满足热方程。在本文中，我们研究了该流体动力学极限周围的平衡波动。我们将波动场定义为作用于歧管上平滑函数的功能，我们表明它们在路径空间中的分布收敛到广义的Ornstein-Uhlenbeck过程。这是通过证明紧密度并表明限制波动满足相应的马丁纳尔问题来完成的。
We consider the Symmetric Exclusion Process on a compact Riemannian manifold, as introduced in van Ginkel and Redig (2020). There it was shown that the hydrodynamic limit satisfies the heat equation. In this paper we study the equilibrium fluctuations around this hydrodynamic limit. We define the fluctuation fields as functionals acting on smooth functions on the manifold and we show that they converge in distribution in the path space to a generalized Ornstein-Uhlenbeck process. This is done by proving tightness and by showing that the limiting fluctuations satisfy the corresponding martingale problem.
