  In this paper, we discuss the convergence rate of empirical processes of
Gaussian processes for a large class of function families. Our main goal is to
show that the tail of the uniform norm of the empirical processes can be
dominated by polynomials. We put forward the properties of Hermite polynomials
which play a crucial role in the proof of main theorems. At the end of the
paper, we show the expectation of the random quantity converging to zero at a
more rapid rate n^{-1/2+{\epsilon}} than ever shown rate n^{-1/3}.
