论文标题
有限图上排除和互换过程的截止
Cutoffs for exclusion and interchange processes on finite graphs
论文作者
论文摘要
在假设图形要么在几何和频谱上收敛到紧凑的度量衡量标准空间，或者它们是与脱离的boolean hyperemean hyperemean hyperemean hyperucubes相同，因此我们证明了有限图上的对称排除和交换过程的临界值的一般定理，并在有限图上进行了交换过程。具体而言，截止时间在$ \ displaystyle t_n =（2γ_1^n）^{ - 1} \ log | v_n | $，其中$γ_1^n $是$ g_n $上的对称随机步行过程的频谱差距。根据前者的假设，我们的定理适用于以下图表上的上述过程，例如：$ d $维离散网格和任何整数尺寸$ d $; $ l $ th的固定$ l $ $ l $，又称$ l $ -Adjacent transiposition Shuffle;及其相似的分形图及其产品。
We prove a general theorem on cutoffs for symmetric exclusion and interchange processes on finite graphs $G_N=(V_N,E_N)$, under the assumption that either the graphs converge geometrically and spectrally to a compact metric measure space, or they are isomorphic to discrete Boolean hypercubes. Specifically, cutoffs occur at times $\displaystyle t_N= (2γ_1^N)^{-1}\log |V_N|$, where $γ_1^N$ is the spectral gap of the symmetric random walk process on $G_N$. Under the former assumption, our theorem is applicable to the said processes on graphs such as: the $d$-dimensional discrete grids and tori for any integer dimension $d$; the $L$-th powers of cycles for fixed $L$, a.k.a. the $L$-adjacent transposition shuffle; and self-similar fractal graphs and products thereof.
