We present , for the first time , a clear N -body realization of the strong mass segregation solution for the stellar distribution around a massive black hole .
We compare our N -body results with those obtained by solving the orbit-averaged Fokker-Planck ( FP ) equation in energy space .
The N -body segregation is slightly stronger than in the FP solution , but both confirm the robustness of the regime of strong segregation when the number fraction of heavy stars is a ( realistically ) small fraction of the total population .
In view of recent observations revealing a dearth of giant stars in the sub-parsec region of the Milky Way , we show that the time scales associated with cusp re-growth are not longer than ( 0.1 - 0.25 ) \times T _ { rlx } ( r _ { h } ) .
These time scales are shorter than a Hubble time for black holes masses M _ { \bullet } \lesssim 4 \times 10 ^ { 6 } M _ { \odot } and we conclude that quasi-steady , mass segregated , stellar cusps may be common around MBHs in this mass range .
Since EMRI rates scale as M _ { \bullet } ^ { - \alpha } , with \alpha \in [ \frac { 1 } { 4 } , 1 ] , a good fraction of these events should originate from strongly segregated stellar cusps .