N-body simulations with AMUSE framework of a BH with mass m_b = 50 M_⊙ immersed with zero velocity in the center, r_b, ini = 1 AU, of a stellar cluster with N_⋆ = 1000, m_⋆ = 0.5 M_⊙, and initial conditions sampled from a Plummer sphere with softening radius, r_c = 0.5 pc. (a) Radial position of the BH with respect to time in a single run. (b) Probability density of the position of the BH for 1000 runs. See text for details.