论文标题
限制在小组中随机步行的预测
Limit Profile for Projections of Random Walks on Groups
论文作者
论文摘要
在马尔可夫链的混合时间理论中，建立截止值是从“不混合”到“混合”的突然过渡。最近，人们不仅在确定截止时间的存在及其混合时间和窗口的顺序方面已经增长，而且还在确定窗口内收敛的确切形状或配置文件。古典技术（例如耦合或$ \ ell_2 $ bunds）通常太粗糙了，无法确定这一点，并且已经在开发一般技术的推动力。 我们以这项工作为基础，从共轭不变的随机步行延伸到某些预测。我们通过在完整的$ n $ graph上用$ k \ asymp n $分析$ k $零件的交换过程来体现我们的方法。这是Teyssier分析的$ k = n $的随机转移卡片的投影。
Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of its mixing time and window, but the exact shape, or profile, of the convergence inside the window. Classical techniques, such as coupling or $\ell_2$-bounds, are typically too crude to establish this and there has been a push to develop general techniques. We build upon this work, extending from conjugacy-invariant random walks on groups to certain projections. We exemplify our method by analysing the $k$-particle interchange process on the complete $n$-graph with $k \asymp n$. This is a projection of the random-transposition card shuffle, which corresponds to $k = n$, analysed by Teyssier.
