论文标题
尖端警察和tips的强盗：偏见随机步行在图表上的碰撞
Tipsy cop and tipsy robber: collisions of biased random walks on graphs
论文作者
论文摘要
由Harris，Insko，Prieto Langarica，Stoisavljevic和Sullivan介绍，\ Emph {Tipsy Cop and Drainden Robber}是警察和强盗游戏的变体，在图形上，强盗只是随机沿着图表随机移动，而警察则朝着Robber固定的固定固定的固定的固定的固定外观，并固定了时间和时间，并将其固定在时间和时间上，并将其定为时间和时间。在本文中，我们对警察和强盗的小费进行了略有不同的解释，我们假设在游戏的任何一轮中都有四种可能的结果：清醒的警察移动，清醒的强盗移动，tip脚（统一随机）通过警察移动，而tip脚（统一随机）则由强盗移动。我们在无限的网格图上研究了这个尖锐的警察和tips脚的强盗游戏，以及某些无限树的家庭，包括$δ$ - 规则的树木％无限的二进制树，其无限路径扎根于每个顶点，以及$δ$ to的树木，植根于$δ$ treegular tree to $δ$ treekular-gequular Tree，其中$δ\ geqegeqΔ$。我们的主要结果分析了这些图表上的COP和强盗的策略。我们以一些指示进行进一步研究。
Introduced by Harris, Insko, Prieto Langarica, Stoisavljevic, and Sullivan, the \emph{tipsy cop and drunken robber} is a variant of the cop and robber game on graphs in which the robber simply moves randomly along the graph, while the cop moves directed towards the robber some fixed proportion of the time and randomly the remainder. In this article, we adopt a slightly different interpretation of tipsiness of the cop and robber where we assume that in any round of the game there are four possible outcomes: a sober cop move, a sober robber move, a tipsy (uniformly random) move by the cop, and a tipsy (uniformly random) move by the robber. We study this tipsy cop and tipsy robber game on the infinite grid graph and on certain families of infinite trees including $δ$-regular trees %infinite binary trees with an infinite path rooted at every vertex, and $δ$-regular trees rooted to a $Δ$-regular tree, where $Δ\geq δ$. Our main results analyze strategies for the cop and robber on these graphs. We conclude with some directions for further study.
