Vector Resonant Relaxation of Stars around a Massive Black Hole
  In the vicinity of a massive black hole, stars move on precessing Keplerian
orbits. The mutual stochastic gravitational torques between the stellar orbits
drive a rapid reorientation of their orbital planes, through a process called
vector resonant relaxation. We derive, from first principles, the correlation
of the potential fluctuations in such a system, and the statistical properties
of random walks undergone by the stellar orbital orientations. We compare this
new analytical approach with effective $N$-body simulations. We also provide a
simple scheme to generate the random walk of a test star's orbital orientation
using a stochastic equation of motion. We finally present quantitative
estimations of this process for a nuclear stellar cluster such as the one of
the Milky Way.
