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The goal of this article is twofold. First, we investigate the linearizedVlasov-Poisson system around a family of spatially homogeneous equilibria in$\mathbb{R}^3$ (the unconfined setting). Our analysis follows classicalstrategies from physics and their subsequent mathematical extensions. The mainnovelties are a unified treatment of a broad class of analytic equilibria andthe study of a class of generalized Poisson equilibria. For the former, thisprovides a detailed description of the associated Green's functions, includingin particular precise dissipation rates (which appear to be new), whereas forthe latter we exhibit explicit formulas.  Second, we review the main result and ideas in our recent work on the fullglobal nonlinear asymptotic stability of the Poisson equilibrium in$\mathbb{R}^3$.

On the stability of homogeneous equilibria in the Vlasov-Poisson system on $\mathbb{R}^3$