报告题目： Branching random walks on relatively hyperbolic groups 

报告人：王龙敏 南开大学  

报告时间：4月20日 2:30-3:30

报告地点： 五教5106 

摘要：

Relatively hyperbolic groups form a broad class of groups in geometric group theory, encompassing hyperbolic groups, free products, and geometrically finite Kleinian groups. They exhibit rich large-scale geometry and admit a natural boundary, introduced by Bowditch, which captures the asymptotic behavior of geodesics and random processes on the group.

In this talk, we discuss the large scale behavior of a transient branching random walks on a non-elementary relatively hyperbolic group.  In this regime the population survives forever, yet eventually leaves every finite subset of the group, and the exponential growth rate of the trace and the Hausdorff dimension of the random limit set of the trace in the Bowditch boundary are both given by the growth rate of the Green function over spheres.  Based on a joint work with Matthieu Dussaule and Wenyuan Yang.