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_Γ. When the defining graph Γ has no SIL-pair (separating intersection of links), we obtain a necessary and sufficient condition for Out(A_Γ) to be acylindrically hyperbolic. As a corollary, if Γ is a random connected graph satisfying a certain probabilistic condition, then Out(A_Γ) is not acylindrically hyperbolic with high probability. When Γ 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_Γ) is closely related to the existence of a specific type of partial conjugations.