  We consider the binary supervised classification problem with the Gaussian
functional model introduced in [7]. Taking advantage of the Gaussian structure,
we design a natural plug-in classifier and derive a family of upper bounds on
its worst-case excess risk over Sobolev spaces. These bounds are parametrized
by a separation distance quantifying the difficulty of the problem, and are
proved to be optimal (up to logarithmic factors) through matching minimax lower
bounds. Using the recent works of [9] and [14] we also derive a logarithmic
lower bound showing that the popular k-nearest neighbors classifier is far from
optimality in this specific functional setting.
