Average entropy of the ranges for simple random walks on discrete groups
主 题: Average entropy of the ranges for simple random walks on discrete groups
报告人: 谢践生副教授 (复旦大学)
时 间: 2014-10-13 15:00-16:00
地 点: welcome欢迎光临威尼斯公司理科一号楼1418（概率论系列报告）
In this talk we first introduce the notion of the average entropy of the ranges for simple random walks on discrete groups, which is inspired by the recent walks of Benjamini et al. It is proved that, (1) The related average sample information converges almost surely (and also in L_1) to the average entropy; (2) The average entropy is always zero for recurrent walks; (3) The average entropy is zero for a transient walk iff the walk is equivalent to a special transient walk on integers; for other transient walks, the average entropy is always positive; (4) The upper semi-continuity of the average entropy in the distribution is also proved.
This is Xin-Xing Chen and Min-Zhi Zhao.
