论文标题
首先在伯特（Bethe）和卡利树（Cayley Trees）上遇到
First encounters on Bethe Lattices and Cayley Trees
论文作者
论文摘要
在这项工作中，我们考虑了固定和/或移动目标A与Bethe Lattices和Cayley树上移动陷阱B之间的第一次遇到问题。分析并比较了两种结构的目标A的生存概率（SP）。在伯特（Bethe）晶格上，结果表明，固定目标仍将延长其生存时间，而在凯利树（Cayley Trees）上，在某些初始位置，目标应移动以延长其生存时间。对移动目标A的平均第一次遇到时间（MFET）进行数值评估，并将其与固定目标A的平均第一通道时间（MFPT）进行比较。解决了不同的初始设置并获得了清晰的边界。这些发现有助于优化延长目标生存时间的策略或与目标的运动和两个步行者的初始位置配置有关的Cayley树上的搜索过程。我们还提出了一种使用少量内存的新方法，用于模拟在Cayley树上的随机步行。
In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe Lattices and Cayley trees. The survival probability (SP) of the target A on the both kinds of structures are analyzed analytically and compared. On Bethe Lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees.
