论文标题
慢速运动方案中的加尔顿 - 瓦特森树上随机偏见的步行量很大
Heavy range of the randomly biased walk on Galton-Watson trees in the slow movement regime
论文作者
论文摘要
我们考虑[HS16]中的慢速运动状态中的树木中随机偏见的随机行走，其潜力是在边界情况下通过分支随机行走发出的。我们研究重型范围至$ n $ th的根源，即访问的边缘数量超过$ k_n $ times。对于$ k_n = n^θ$，带有$θ\ in（0,1）$，我们获得了重新缩放重范围的概率的收敛性，这改善了[ad20]的结果。
We consider the randomly biased random walk on trees in the slow movement regime as in [HS16], whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the $n$-th return to the root, i.e., the number of edges visited more than $k_n$ times. For $k_n=n^θ$ with $θ\in(0,1)$, we obtain the convergence in probability of the rescaled heavy range, which improves one result of [AD20].
