报告题目:Generalized birth-death chains on hyperbolic graphs and induced energy forms on their boundaries

报告人：孔诗磊（四川大学）

报告时间：2022年12月30日（周五）15:00-16:00

报告地点：腾讯会议：589-361-543

摘要：As a generalization of the birth-death chains on nonnegative integers, we introduce a class of reversible Markov chains (GBDCs) on hyperbolic graphs, and analyze the induced energy forms on their boundaries. With certain assumptions on the birth-death ratios, we show that the Martin boundary is homeomorphic to the Gromov boundary of the graph. Applying a new technique of graph expansion, we prove the volume doubling property of the hitting distribution, and obtain a two-sided estimate of the Naım kernel. In addition, we provide some examples of GBDCs related to fractal analysis, and show the existence of GBDCs on every hyperbolic graph with bounded degree.

报告人简介：孔诗磊，男，汉族，2012年本科毕业于浙江大学，2017年博士毕业于香港中文大学，2017–2022年在德国比勒菲尔德大学做博士后。现任四川大学数学学院副研究员，主要研究方向为离散随机游动和分形分析，代表作包括自相似集的Gromov双曲图结构、随机游动及诱导能量估计等。

邀请人：金永阳，曹军