  We derive an integration by parts formula for functionals of determinantal
processes on compact sets, completing the arguments of [4]. This is used to
show the existence of a configuration-valued diffusion process which is
non-colliding and admits the distribution of the determinantal process as
reversible law. In particular, this approach allows us to build a concrete
example of the associated diffusion process, providing an illustration of the
results of [4] and [30].
