Sublinearly Morse boundary of \(\mathrm{CAT}(0)\) admissible groups (Q6565831)

Morse boundaries are group invariants and metrizable topological spaces, they are similar to the Gromov boundary of hyperbolic spaces and provide insights into groups that contain hyperbolic-like features. One of the most interesting properties of sublinearly Morse boundaries is that they reveal the asymptotic behavior of random walks on the associated groups.\N\NLet \(G\) be an admissible group acting geometrically on a \(\mathrm{CAT}(0)\) space \(X\). In the paper under review, the authors show that \(G\) is a hierarchically hyperbolic space and its \(\kappa\)-Morse boundary \((\partial_{\kappa}G, \nu)\) is a model for the Poisson boundary of \((G, \mu)\), where \(\nu\) is the hitting measure associated to the random walk driven by \(\mu\) (see also [\textit{V. A. Kaimanovich}, Ann. Math. (2) 152, No. 3, 659--692 (2000; Zbl 0984.60088)]).