Branching random walks on relatively hyperbolic groups
报告人： 杨文元（北京大学）、王龙敏（南开大学）
时间：2026-03-23 14:00-15:00
地点：智华楼四元厅-225
Abstract:
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 branching random walks on a non-elementary relatively hyperbolic group Γ. The model is obtained by combining a symmetric, finitely supported admissible random walk on Γ with an offspring distribution of mean r. When 1
In this two-part talk, we first describe the background and motivation, and then explain two results concerning the large-scale geometry of the trace of the branching random walk. First, we show that the exponential growth rate of the trace is exactly the growth rate ω(r) of the Green function over spheres of the underlying random walk. Second, if Λ(r) denotes the random limit set of the trace in the Bowditch boundary, then its Hausdorff dimension is almost surely equal to an explicit constant multiple of ω(r).
About the Speaker:
杨文元是北京大学数学系的教授，研究方向为几何群论和低维拓扑学。王龙敏，南开大学统计与数据科学学院教授，主要研究方向为群上的概率模型。
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