  In this paper, we study exponentially fast mixing induced/enhanced by gravity
and stochastic boundary in the kinetic theory of Vlasov equations. We consider
the Vlasov equations with and without a vertical magnetic field inside a
horizontally-periodic 3D half-space equipped with a non-isothermal diffusive
reflection boundary condition of bounded continuous boundary temperature at the
bottom. We construct both stationary solutions and global-in-time dynamical
solutions in $L^\infty$. We prove that moments of a dynamical fluctuation
around the steady solutions decay exponentially fast in $L^\infty$. As a key of
this proof, we establish a uniform bound of so-called residual measures
independently of the bouncing number of stochastic characteristics, by
constructing a continuous stationary outgoing boundary flux which is strictly
positive almost everywhere.
