Institute for Advanced Study Informal Astrophysics Seminar - TITLE ADDED

Galactic nuclei and the Massive black holes (MBHs) in their centers are rich environments, where the complex stellar dynamics plays an important role in many physical phenomena. We show that the standard description of the two-body relaxation, around an MBH, as a diffusion process, is incomplete. We derived a non-perturbative solution for energy relaxation as an anomalous diffusion process, and a robust estimation technique to measure it in N-body simulations. We also show how the dynamics of a nearly-Keplerian N-body system, where the angular momentum evolution is accelerated by resonant relaxation, can be described and studied in a formal statistical mechanics framework. In this framework the background potential is described as a correlated Gaussian noise. We obtained the leading order, phase-averaged stochastic equations of motion and derived an effective Fokker-Plank equation for a general correlated Gaussian noise. We combine the Fokker-Plank description of two-body relaxation and resonant relaxation to study the loss-cone dynamics in Galactic nuclei.