  We study the Small Ball Probabilities (SBPs) of Gaussian rough paths. While
many works on rough paths study the Large Deviations Principles (LDPs) for
stochastic processes driven by Gaussian rough paths, it is a noticeable gap in
the literature that SBPs have not been extended to the rough path framework.
  LDPs provide macroscopic information about a measure for establishing
Integrability type properties. SBPs provide microscopic information and are
used to establish a locally accurate approximation for a measure. Given the
compactness of a Reproducing Kernel Hilbert space (RKHS) ball, its metric
entropy provides invaluable information on how to approximate the law of a
Gaussian rough path.
  As an application, we are able to find upper and lower bounds for the rate of
convergence of an empirical rough Gaussian measure to its true law in
pathspace.
