论文标题
用$ o（n）$交换的伯诺利 - 拉普拉斯模型中的截止
Cutoff in the Bernoulli-Laplace model with $O(n)$ swaps
论文作者
论文摘要
本文考虑了$（n，k）$ -Bernoulli-laplace模型在有两个urn的情况下，红球的总数相同，并且每个步骤的选择$ k $的数量与每个urn中的球$ n $相同的渐近顺序。我们的主要重点是相应的马尔可夫链的大型行为跟踪给定的urn中红球的数量。在对比率$ k/n $的渐近行为为$ n \ rightarrow \ infty $的合理假设下，建立了总变化距离的临界值。还提供了一个截止窗口。这些结果尤其是部分解决了埃斯康纳齐斯和内斯托里迪提出的一个开放问题。
This paper considers the $(n,k)$-Bernoulli--Laplace model in the case when there are two urns, the total number of red and white balls is the same, and the number of selections $k$ at each step is on the same asymptotic order as the number of balls $n$ in each urn. Our main focus is on the large-time behavior of the corresponding Markov chain tracking the number of red balls in a given urn. Under reasonable assumptions on the asymptotic behavior of the ratio $k/n$ as $n\rightarrow \infty$, cutoff in the total variation distance is established. A cutoff window is also provided. These results, in particular, partially resolve an open problem posed by Eskenazis and Nestoridi.
