Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the evolution of orbital angular momentum by resonant relaxation. This drives many phenomena near MBHs, such as extreme mass-ratio gravitational wave inspirals, the warping of accretion disks, and the formation of exotic stellar populations. We present here a formal statistical mechanics framework to analyze such systems, where the background potential is described as a correlated Gaussian noise. We derive the leading order, phase-averaged 3D stochastic Hamiltonian equations of motion, for evolving the orbital elements of a test star, and obtain the effective Fokker-Planck equation for a general correlated Gaussian noise, for evolving the stellar distribution function. We show that the evolution of angular momentum depends critically on the temporal smoothness of the background potential fluctuations. We show that in the presence of smooth noise, the evolution of the normalized angular momentum a relativistic test star, undergoing Schwarzschild (in-plane) General Relativistic precession, is exponentially suppressed due to the adiabatic invariance of the precession against the slowly varying random background torques. This results in an effective Schwarzschild precession-induced barrier in angular momentum.