论文标题
广义$ n $ n $ urn ehrenfest模型的流体动力学
Hydrodynamics of the generalized $N$-urn Ehrenfest model
论文作者
论文摘要
在本文中，我们关注的是$ n $ n $ urn ehrenfest的型号，该模型在$ n $ box之间保持独立的随机步行均匀地铺设在$ [0，1] $上。在适当地缩放上述随机步行的过渡速率函数之后，我们得出了模型的流体动力学极限，即模型的经验度量的大数量定律遵循，在一个假设下，每个盒子中的初始球数独立于poisson分布。我们表明，模型的经验度量薄弱地收敛到由积分方程驱动的密度的确定性度量。此外，我们得出了模型的非平衡波动，即从上述流体动力学极限中的中心极限定理。我们表明，该模型的非平衡波动是由测量值征值的广义O-U过程驱动的。最后，我们证明了与上述随机步行的$ [0，1] \ times [0，1] $ [0，1] $ [0，1] $从$ [0，1] \ $ [0， +\ fty）$的假设下的较大偏差原理，这是上述随机步行的产物，是两个边际功能的产物，来自$ [0，1] $ [0，1] $ [0，1] $ [0，1] $ [0， +\ f \ f infty）$。
In this paper we are concerned with a generalized $N$-urn Ehrenfest model, where balls keeps independent random walks between $N$ boxes uniformly laid on $[0, 1]$. After a proper scaling of the transition rates function of the aforesaid random walk, we derive the hydrodynamic limit of the model, i.e., the law of large numbers which the empirical measure of the model follows, under an assumption where the initial number of balls in each box independently follows a Poisson distribution. We show that the empirical measure of the model converges weakly to a deterministic measure with density driven by an integral equation. Furthermore, we derive non-equilibrium fluctuation of the model, i.e, the central limit theorem from the above hydrodynamic limit. We show that the non-equilibrium fluctuation of the model is driven by a measure-valued time-inhomogeneous generalized O-U process. At last, we prove a large deviation principle from the hydrodynamic limit under an assumption where the transition rates function from $[0, 1]\times [0, 1]$ to $[0, +\infty)$ of the aforesaid random walk is a product of two marginal functions from $[0, 1]$ to $[0, +\infty)$.
