  Random matrix theory can be used to describe the transport properties of a
chaotic quantum dot coupled to leads. In such a description, two approaches
have been taken in the literature, considering either the Hamiltonian of the
dot or its scattering matrix as the fundamental random quantity of the theory.
In this paper, we calculate the first four moments of the distribution of the
scattering matrix of a chaotic quantum dot with a time-dependent potential,
thus establishing the foundations of a ``random scattering matrix approach''
for time-dependent scattering. We consider the limit that the number of
channels $N$ coupling the quantum dot the reservoirs is large. In that limit,
the scattering matrix distribution is almost Gaussian, with small non-Gaussian
corrections. Our results reproduce and unify results for conductance and pumped
current previously obtained in the Hamiltonian approach. We also discuss an
application to current noise.
