Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups

We study the acylindrical hyperbolicity of the outer automorphism group of a right-angled Artin group A_. When the defining graph has no SIL-pair (separating intersection of links), we obtain a necessary and sufficient condition for Out (A_) to be acylindrically hyperbolic. As a corollary, if is a random connected graph satisfying a certain probabilistic condition, then Out (A_) is not acylindrically hyperbolic with high probability. When has a maximal SIL-pair system, we derive a classification theorem for partial conjugations. Such a classification theorem allows us to show that the acylindrical hyperbolicity of Out (A_) is closely related to the existence of a specific type of partial conjugations.