確率論セミナー


2019/6/11(Tue)

16:30--18:00 理学部 E404/406/408 大セミナー室数学教室 大セミナー室 (E404)

難波 隆弥

立命館大学

Moderate deviation principles on covering graphs of polynomial volume growth and its application

In this talk, moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed from a geometric perspective. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. Finally, we apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all a.s. limit points of the normalized random walks.