论文标题
混合在动态随机群集上随机步行的时间
Mixing time of random walk on dynamical random cluster
论文作者
论文摘要
我们研究一个随机步行者的混合时间，该步行者在侧长n的D维圆环上移动到动态随机群集模型中。在此模型中，遵循带有参数p，q的随机群集模型的glauber动力学之间的速率μbets开关。同时，沃克以1个简单的随机步行在圆环上跳跃，但只允许横穿开放边缘。我们表明，对于足够小的p，随机助行器的混合时间为n^2/μ。在我们的证明中，我们通过对环境的多尺度分析来构建非马克维亚耦合，我们认为这可能更广泛地适用。
We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate μbetween open and closed, following a Glauber dynamics for the random cluster model with parameters p,q. At the same time, the walker jumps at rate 1 as a simple random walk on the torus, but is only allowed to traverse open edges. We show that for small enough p the mixing time of the random walker is of order n^2/μ. In our proof we construct of a non-Markovian coupling through a multi-scale analysis of the environment, which we believe could be more widely applicable.
