论文标题
与开放边界的简单排除过程的混合时间
Mixing times for the simple exclusion process with open boundaries
论文作者
论文摘要
我们研究了允许粒子在端点进入和退出的段的对称和不对称简单排除过程的混合时间。我们考虑不同的制度，具体取决于输入和退出率以及批量的利率，并表明该过程显示前切口前，在某些情况下显示出截止。我们的主要贡献是研究与开放边界的不对称简单排除过程的混合时间。我们表明，根据选择边界参数的选择，混合时间的顺序可以在段的大小上是线性的或指数的，这证明了与封闭段的过程相比，具有开放界限的简单排除过程的截然不同（且更丰富）的行为。我们的参数将耦合，二等粒子和审查技术与当前估计结合在一起。一个新颖的想法是使用多物种粒子参数，其中粒子只遵守部分排序。
We study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the rates in the bulk, and show that the process exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time can be linear or exponential in the size of the segment depending on the choice of the boundary parameters, proving a strikingly different (and richer) behavior for the simple exclusion process with open boundaries than for the process on the closed segment. Our arguments combine coupling, second class particle and censoring techniques with current estimates. A novel idea is the use of multi-species particle arguments, where the particles only obey a partial ordering.
