论文标题
在具有开放边界的图表上排除过程的截止
Cutoffs for exclusion processes on graphs with open boundaries
论文作者
论文摘要
在自然假设下，我们证明了具有开放边界的对称简单排除过程的临界值的一般定理，这是在自然假设上以几何和频谱收敛到具有DIRICHLET边界条件的紧凑度量测量空间。我们的定理在各种设置上都是有效的，包括但不限于：每个整数尺寸$ d $的$ d $维格;及其相似的分形图及其产品。我们的证明方法是确定密度波动场的重新缩放版本 - 截止Martingale--这使我们能够证明与Wilson方法获得的下限匹配的混合时间上限。
We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space with Dirichlet boundary condition. Our theorem is valid on a variety of settings including, but not limited to: the $d$-dimensional grid for every integer dimension $d$; and self-similar fractal graphs and products thereof. Our method of proof is to identify a rescaled version of the density fluctuation field---the cutoff martingale---which allows us to prove the mixing time upper bound that matches the lower bound obtained via Wilson's method.
