arXiv subjects

Vivian He

Publications and source records attributed to Vivian He.

3 recordsLinked to original sources

arXiv2024

Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures

We show that the Morse boundary of a Morse local-to-global group is $\sigma$-compact. Moreover, we show that the converse holds for small cancellation groups. As an application, we show that the Morse boundary of a non-hyperbolic, Morse local-to-global group that has contraction does not admit a non-trivial stationary measure. In fact, we show that any stationary measure on a geodesic boundary of such a groups needs to assign measure zero to the Morse boundary. Unlike previous results, we do not need any assumptions on the stationary measures considered.

math.GR↗

arXiv2023

Random walks on groups and superlinear divergent geodesics

In this paper, we study random walks on groups that contain superlinear divergent geodesics, in the line of thoughts of Goldsborough-Sisto. The existence of a superlinear divergent geodesic is a quasi-isometry invariant which allows us to execute Gouëzel's pivoting technique. We develop the theory of superlinear divergence and establish a central limit theorem for random walks on these groups.

math.GT↗

arXiv2022

Equivalent Topologies on the Contracting Boundary

The contracting boundary of a proper geodesic metric space generalizes the Gromov boundary of a hyperbolic space. It consists of contracting geodesics up to bounded Hausdorff distances. Another generalization of the Gromov boundary is the $κ$-Morse boundary with a sublinear function $κ$. The two generalizations model the Gromov boundary based on different characteristics of geodesics in Gromov hyperbolic spaces. It was suspected that the $κ$-Morse boundary contains the contracting boundary. We will prove this conjecture: when $κ=1$ is the constant function, the 1-Morse boundary and the contracting boundary are equivalent as topological spaces.

math.GT↗