论文标题
在扩展器图上随机行走的局部中央限制定理
A local central limit theorem for random walks on expander graphs
论文作者
论文摘要
建立马尔可夫连锁店的中心限制定理的历史悠久。曼恩证明了具有光谱间隙的链条的定量界限，并在后来进行了完善。最近，在扩展器图上随机步行的总变异距离的收敛速率，这些距离通常用于生成满足所需的假拟南索属性的序列。我们证明了一个局部中央限制定理，其在扩展器图上随机步行的收敛速率具有明显的收敛速度，并为总变化距离提供了改进的结合。
There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were obtained for random walks on expander graphs, which are often used to generate sequences satisfying desirable pseudorandom properties. We prove a local central limit theorem with an explicit rate of convergence for random walks on expander graphs, and derive an improved bound for the total variation distance.
