论文标题
$ n $ n $ urn线性系统的流体动力学
Hydrodynamics of a class of $N$-urn linear systems
论文作者
论文摘要
在本文中，我们关注的是一类$ n $ urn线性系统的流体动力学，其中包括选民模型，成对对称的排除过程和$ n $ urns作为特殊情况的二进制联系路径过程。 We show that the hydrodynamic limit of our process is driven by a $\left(C[0,1]\right)^\prime$-valued linear ordinary differential equation and the fluctuation of our process, i.e, central limit theorem from the hydrodynamic limit, is driven by a $\left(C[0, 1]\right)^\prime$-valued Ornstein-Uhlenbeck process.为了获得高于主要结果，我们需要几个替代引理。 Chapman-Kolmogorov方程线性系统的扩展在这些替代引理的证明中起关键作用。
In this paper we are concerned with hydrodynamics of a class of $N$-urn linear systems, which include voter models, pair-symmetric exclusion processes and binary contact path processes on $N$ urns as special cases. We show that the hydrodynamic limit of our process is driven by a $\left(C[0,1]\right)^\prime$-valued linear ordinary differential equation and the fluctuation of our process, i.e, central limit theorem from the hydrodynamic limit, is driven by a $\left(C[0, 1]\right)^\prime$-valued Ornstein-Uhlenbeck process. To derive above main results, we need several replacement lemmas. An extension in linear systems of Chapman-Kolmogorov equation plays key role in proofs of these replacement lemmas.
