  Upper bounds for rates of convergence of posterior distributions associated
to Gaussian process priors are obtained by van der Vaart and van Zanten in [14]
and expressed in terms of a concentration function involving the Reproducing
Kernel Hilbert Space of the Gaussian prior. Here lower-bound counterparts are
obtained. As a corollary, we obtain the precise rate of convergence of
posteriors for Gaussian priors in various settings. Additionally, we extend the
upper-bound results of [14] about Riemann-Liouville priors to a continuous
family of parameters.
