Sublinearly Morseness in Higher Rank Symmetric Spaces

The goal of this paper is to develop a theory of “sublinearly Morse boundary” and prove a corresponding sublinearly Morse lemma in higher rank symmetric space of non-compact type. This is motivated by the work of Kapovich-Leeb-Porti and the theory of sublinearly Morse quasi-geodesics developed in the context of CAT(0) geometry.