Rate of change in angular momentum ﹩\langle {({\rm{\Delta }}J)}^{2}\rangle /({J}_{{\rm{c}}}^{2}{\rm{\Delta }}T)﹩ for different time intervals ﹩{\rm{\Delta }}T﹩. We compare our analytical calculation Equation (24) (dashed lines) to the one obtained for Hamers et al. (2014) test particle simulations (circles with error bars). As ﹩{\rm{\Delta }}T﹩ becomes larger, ﹩{\rm{\Delta }}J/({J}_{{\rm{c}}}{\rm{\Delta }}T)﹩ converges to the diffusion coefficient (solid line). The diffusion coefficients were evaluated for an isotropic BW cusp ﹩f(E)\propto {E}^{1/2}﹩ of 10 solar mass stars around an MBH of ﹩{M}_{\bullet }=4\times {10}^{6}{M}_{\odot }﹩ and a total mass of ﹩4.8\times {10}^{4}{M}_{\odot }﹩ within ﹩r=0.2\,\mathrm{pc}﹩, for SMA in the range 9.4–11.1 Mpc, where ﹩{T}_{{\rm{c}}}\approx 1107P(a)﹩.