论文标题
随机卡片的过程
A Random Card Shuffling Process
论文作者
论文摘要
考虑带有$ N $红牌和$ N $黑卡的$ 2N $卡的随机洗牌甲板。我们研究了从随机洗牌的甲板到甲板的平均移动次数，该甲板通过执行以下动作而交替进行颜色：如果顶部卡和甲板的底部卡在颜色上有所不同，则将顶部卡放在甲板底部的顶部卡，否则，将顶部卡在甲板中随机插入。我们使用组合学，概率和线性代数的工具将该过程建模为有限的马尔可夫链。
Consider a randomly shuffled deck of $2n$ cards with $n$ red cards and $n$ black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck that alternates in color by performing the following move: If the top card and the bottom card of the deck differ in color place the top card at the bottom of the deck, otherwise, insert the top card randomly in the deck. We use tools from combinatorics, probability, and linear algebra to model this process as a finite Markov chain.
