论文标题
在加尔顿 - 瓦特森树上随机随机步行的最大本地时间
Maximal local time of randomly biased random walks on a Galton-Watson tree
论文作者
论文摘要
我们考虑在分支随机行走给出的随机环境中，在植根树上进行随机步行。直到第一次返回根，它的边缘本地时间就形成了多类型的Galton-Watson树，具有无限多种类型。当步行是扩散的或不足的时，通过研究这条加尔顿 - 瓦特森树的最大类型，我们根据退火定律建立了在n次远景期间这次步行的最大当地时代的渐近行为。
We consider a recurrent random walk on a rooted tree in random environment given by a branching random walk. Up to the first return to the root, its edge local times form a Multi-type Galton-Watson tree with countably infinitely many types. When the walk is the diffusive or sub-diffusive, by studying the maximal type of this Galton-Watson tree, we establish the asymptotic behaviour of the largest local times of this walk during n excursions, under the annealed law.
