  The propagation of chaos and associated law of large numbers for mean-field
interacting age-dependent Hawkes processes (when the number of processes n goes
to +$\infty$) being granted by the study performed in (Chevallier, 2015), the
aim of the present paper is to prove the resulting functional central limit
theorem. It involves the study of a measure-valued process describing the
fluctuations (at scale n --1/2) of the empirical measure of the ages around its
limit value. This fluctuation process is proved to converge towards a limit
process characterized by a limit system of stochastic differential equations
driven by a Gaussian noise instead of Poisson (which occurs for the law of
large numbers limit).
