  In this paper, we focus on the construction of a hybrid scheme for the
approximation of non-Maxwellian kinetic models with uncertainties. In the
context of multiagent systems, the introduction of a kernel at the kinetic
level is useful to avoid unphysical interactions. The methods here proposed,
combine a direct simulation Monte Carlo (DSMC) in the phase space together with
stochastic Galerkin (sG) methods in the random space. The developed schemes
preserve the main physical properties of the solution together with accuracy in
the random space. The consistency of the methods is tested with respect to
surrogate Fokker-Planck models that can be obtained in the quasi-invariant
regime of parameters. Several applications of the schemes to non-Maxwellian
models of multiagent systems are reported.
