树上一次加强随机游动的分枝破产数和临界参数
The branching-ruin number and the critical parameter of once-reinforced random walk on trees
摘要：
本文的动机是研究一类树上自交互随机游动（包括曾经加强的随机游动）的复发/瞬时相变。为了这个目的，我们定义了一个量，我们称之为树的分支破产数，它提供了（在Furstenberg，1970年和Lyons，1990年的精神）一种自然的方法来测量多项式增长的树。证明了树的分枝破产数等于一次强化随机游动的常返性/瞬时性的临界参数。我们定义了一个尖锐的和有效的（即可计算的）标准表征递归/瞬态的一个更大的类的自相互作用的走在树上，提供完整的图片为他们的相变。
英文摘要：
The motivation for this paper is the study of the phase transition for recurrence/transience of a class of self-interacting random walks on trees, which includes the once-reinforced random walk. For this purpose, we define a quantity, that we call the branching-ruin number of a tree, which provides (in the spirit of Furstenberg, 1970, and Lyons, 1990) a natural way to measure trees with polynomial growth. We prove that the branching-ruin number of a tree is equal to the critical parameter for the recurrence/transience of the once-reinforced random walk. We define a sharp and effective (i.e. computable) criterion characterizing the recurrence/transience of a larger class of self-interacting walks on trees, providing the complete picture for their phase transition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
