论文标题
远程对称排除的流体动力行为具有缓慢的障碍：超级避难所
Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: superdiffusive regime
论文作者
论文摘要
我们分析了在慢速屏障存在下跳远对称排除过程的流体动力学行为。跳跃率由具有无限差异的对称过渡概率$ p（\ cdot）$给出。当跳跃从$ \ mathbb {z} _ { - }^{*} $到$ \ mathbb n $发生时，费率被因子$αn^{ - β} $减慢（带有$α> 0 $和$β\ egq \ geq 0 $）。我们在$ \ mathbb r^*$上获得了几个根据区域分数laplacian给出的几个部分微分方程，并且具有不同的边界条件。出乎意料的是，与扩散制度相反，我们获得了不同的制度，具体取决于$α= 1 $（所有债券的利率相同）还是$α\ neq 1 $。
We analyse the hydrodynamical behavior of the long jumps symmetric exclusion process in the presence of a slow barrier. The jump rates are given by a symmetric transition probability $p(\cdot)$ with infinite variance. When jumps occur from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$ the rates are slowed down by a factor $αn^{-β}$ (with $α>0$ and $β\geq 0$). We obtain several partial differential equations given in terms of the regional fractional Laplacian on $\mathbb R^*$ and with different boundary conditions. Surprisingly, in opposition to the diffusive regime, we get different regimes depending on whether $α=1$ (all bonds with the same rate) or $α\neq 1$.
