  We design a deterministic particle method for the solution of the spatially
homogeneous Landau equation with uncertainty. The deterministic particle
approximation is based on the reformulation of the Landau equation as a formal
gradient flow on the set of probability measures, whereas the propagation of
uncertain quantities is computed by means of a sg representation of each
particle. This approach guarantees spectral accuracy in uncertainty space while
preserving the fundamental structural properties of the model: the positivity
of the solution, the conservation of invariant quantities, and the entropy
production. We provide a regularity results for the particle method in the
random space. We perform the numerical validation of the particle method in a
wealth of test cases.

Numerical Analysis;Numerical Analysis;Analysis of PDEs;Computational Physics;Plasma Physics