论文标题
对称随机环境中简单排除过程的流体动力限制通过二元性和均匀化
Hydrodynamic limit of simple exclusion processes in symmetric random environments via duality and homogenization
论文作者
论文摘要
我们考虑在$ \ mathbb {r}^d $的随机局部有限子集上进行连续时随机步行，并具有随机对称跳跃概率。跳跃范围可能是无限的。我们假设某些第二张条件，上述随机性是由组$ \ mathbb {g} = \ mathbb {r}^d $或$ \ mathbb {g} = \ mathbb {z}^d $不变的。然后，我们添加了一个位点排斥相互作用，从而使粒子系统成为简单的排除过程。我们表明，对于几乎所有环境，在扩散的时空重新缩放下，该系统在路径空间中表现出流体动力的极限。流体动力方程是非随机的，并且受单个随机步行的有效同质矩阵$ d $的控制，可以退化。以上结果涵盖了包括例如由$ \ mathbb {z}^d $以及Crystal Lattices上的随机电导模型和Crystal Lattices上（可能具有长电导率），Mott可变范围跳跃，简单的随机步行，在Delaunay三角形上进行随机步行，对超批判性渗透簇进行随机步行。
We consider continuous-time random walks on a random locally finite subset of $\mathbb{R}^d$ with random symmetric jump probability rates. The jump range can be unbounded. We assume some second--moment conditions and that the above randomness is left invariant by the action of the group $\mathbb{G}=\mathbb{R}^d$ or $\mathbb{G}=\mathbb{Z}^d$. We then add a site-exclusion interaction, thus making the particle system a simple exclusion process. We show that, for almost all environments, under diffusive space-time rescaling the system exhibits a hydrodynamic limit in path space. The hydrodynamic equation is non-random and governed by the effective homogenized matrix $D$ of the single random walk, which can be degenerate. The above result covers a very large family of models including e.g. simple exclusion processes built from random conductance models on $\mathbb{Z}^d$ and on crystal lattices (possibly with long conductances), Mott variable range hopping, simple random walks on Delaunay triangulations, random walks on supercritical percolation clusters.
