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For the Vlasov-Poisson-Boltzmann equations with random uncertainties from theinitial data or collision kernels, we proved the sensitivity analysis andenergy estimates uniformly with respect to the Knudsen number in the diffusivescaling using hypocoercivity method. As a consequence, we also justified theincompressible Navier-Stokes-Poisson limit with random inputs. In particular,for the first time, we obtain the precise convergence rate {\em without}employing any results based on Hilbert expansion. We not only generalized theprevious deterministic Navier-Stokes-Poisson limits to random initial datacase, also improve the previous uncertainty quantification results to the casewhere the initial data include both kinetic and fluid parts.

Sensitivity analysis and incompressible Navier-Stokes-Poisson limit of Vlasov-Poisson-Boltzmann equations with uncertainty