The study of uncertainty propagation is of fundamental importance in plasma physics simulations. However, the construction of numerical methods is challenging due to the high-dimensionality of the problem, the presence of multiple space-time scales, and the constraints imposed by the need to preserve certain relevant physical properties. In the present talk we present a novel class of methods based on a stochastic-Galerkin (sG) approximation of the uncertain particles' position and velocity. We first describe the method in the case of the Vlasov-Poisson system with a BGK term describing plasma collisions and than consider the challenging case where collisions are characterized by the Landau-Fokker-Planck operator. We show that the sG particle method preserves the main physical properties of the problem, such as conservations and positivity of the solution, while achieving spectral accuracy for smooth solutions in the random space. Furthermore, in the fluid limit we discuss how to design the sG particle solver in order to possess the asymptotic-preserving property, thus avoiding the loss of hyperbolicity typical of conventional sG methods based on finite differences or finite volumes. References 1. A. Medaglia, L. Pareschi, M. Zanella, Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties, J. Comp. Phys. Volume 479, 112011, 2023 2. A. Medaglia, L. Pareschi, M. Zanella, Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data, preprint arXiv:2306.07701, 2023 I will arrive on Monday, February 22, in the afternoon. Therefore, I will be able to parti