Stochastic dynamics of determinantal processes by integration by parts

We derive an integration by parts formula for functionals of de- terminantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a conguration-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]. 1