  For linear transport and radiative heat transfer equations with random
inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving
stochastic Galerkin schemes that allow efficient computation for the problems
that contain both uncertainties and multiple scales. Compared with previous
methods for these problems, our new method use the implicit-explicit (IMEX)
time discretization to gain higher order accuracy, and by using a modified
diffusion operator based penalty method, a more relaxed stability condition--a
hyperbolic, rather than parabolic, CFL stability condition, is achieved in the
case of small mean free path in the diffusive regime. The stochastic
Asymptotic-Preserving property of these methods will be shown asymptotically,
and demonstrated numerically, along with computational cost comparison with
previous methods.
