Sublinearly Morse boundary of CAT(0) admissible groups

Abstract

We show that if 𝐺 is an admissible group acting geometrically on a CAT ⁡ ( 0 ) \operatorname{CAT}(0) space 𝑋, then 𝐺 is a hierarchically hyperbolic space and its 𝜅-Morse boundary ( ∂ κ G , ν ) (\partial_{\kappa}G,\nu) is a model for the Poisson boundary of ( G , μ ) (G,\mu) , where 𝜈 is the hitting measure associated to the random walk driven by 𝜇.