论文标题
恰好可溶解的自诱饵晶格步行。第一部分：捕获梯子图
Exactly-Solvable Self-Trapping Lattice Walks. Part I: Trapping in Ladder Graphs
论文作者
论文摘要
越来越多的自我避免行走（GSAW）是一个随机过程，它从晶格上的原点开始，并通过随机占据无人居住的相邻晶格位点而生长。一个足够长的GSAW将到达一个状态，在该州中，所有相邻地点已经被步行所占据并被困住，从而终止了过程。从经验上可以从模拟中知道，在平均晶格上，这是在平均71个步骤之后发生的。在一系列两部分的手稿的第一部分中，我们考虑了简化的晶格几何形状，只有两个位点（“梯子”），并得出生成函数，以供GSAW捕获的概率分布。我们证明，在平均17个步骤后，在平均值的梯子上进行自捕捉的步行将被困在三角梯子上，将在平均941/48（〜19.6步）之后发生。我们讨论了我们的结果的其他含义，以理解“无限” GSAW中的陷阱。
A growing self-avoiding walk (GSAW) is a stochastic process that starts from the origin on a lattice and grows by occupying an unoccupied adjacent lattice site at random. A sufficiently long GSAW will reach a state in which all adjacent sites are already occupied by the walk and become trapped, terminating the process. It is known empirically from simulations that on a square lattice, this occurs after a mean of 71 steps. In Part I of a two-part series of manuscripts, we consider simplified lattice geometries only two sites high ("ladders") and derive generating functions for the probability distribution of GSAW trapping. We prove that a self-trapping walk on a square ladder will become trapped after a mean of 17 steps, while on a triangular ladder trapping will occur after a mean of 941/48 (~19.6 steps). We discuss additional implications of our results for understanding trapping in the "infinite" GSAW.
