论文标题
远程对称排除的扩散波动和缓慢的屏障
Diffusive fluctuations of long-range symmetric exclusion with a slow barrier
论文作者
论文摘要
在本文中，我们获得了跳远的$ \ Mathbb {z} $中对称排除过程的平衡波动。从$ x $到$ y $跳跃的过渡概率与$ | x-y |^{ - γ-1} $成比例。在这里，我们限于选择$γ\ geq 2 $，以便系统具有扩散行为。此外，当粒子在$ \ mathbb {z} _ { - }^{*} $和$ \ mathbb n $之间移动时，$αn^{ - β} $将跳跃速度放慢速度，其中$α> 0 $，$α> 0 $，$β\ geq 0 $ n $ n $ and $ n $是量表参数。根据$β$和$γ$的值，我们获得了几个随机部分微分方程，对应于没有边界条件的热方程，或者与罗宾边界条件或诺伊曼边界条件。
In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in $\mathbb{Z}$ with long jumps. The transition probability of the jump from $x$ to $y$ is proportional to $|x-y|^{-γ-1}$. Here we restrict to the choice $γ\geq 2$ so that the system has a diffusive behavior. Moreover, when particles move between $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, the jump rates are slowed down by a factor $αn^{-β}$, where $α>0$, $β\geq 0$ and $n$ is the scaling parameter. Depending on the values of $β$ and $γ$, we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions.
