  We derive the stationary probability distribution for a non-equilibrium
system composed by an arbitrary number of degrees of freedom that are subject
to Gaussian colored noise and a conservative potential. This is based on a
multidimensional version of the Unified Colored Noise Approximation. By
comparing theory with numerical simulations we demonstrate that the theoretical
probability density quantitatively describes the accumulation of active
particles around repulsive obstacles. In particular, for two particles with
repulsive interactions, the probability of close contact decreases when one of
the two particle is pinned. Moreover, in the case of isotropic confining
potentials, the radial density profile shows a non trivial scaling with radius.
Finally we show that the theory well approximates the "pressure" generated by
the active particles allowing to derive an equation of state for a system of
non-interacting colored noise-driven particles.
