Observational signatures of the black hole Mass Distribution in the
  Galactic Center
  We simulate the star cluster, made of stars in the main sequence and
different black hole (BH) remnants, around SgrA* at the center of the Milky Way
galaxy. Tracking stellar evolution, we find the BH remnant masses and construct
the BH mass function. We sample 4 BH species and consider the impact of the
mass-function in the dynamical evolution of system. Starting from an initial 6
dimensional family of parameters and using an MCMC approach, we find the best
fits to various parameters of model by directly comparing the results of the
simulations after $t = 10.5$ Gyrs with current observations of the stellar
surface density, stellar mass profile and the mass of SgrA*. Using these
parameters, we study the dynamical evolution of system in detail. We also
explore the mass-growth of SgrA* due to tidally disrupted stars and swallowed
BHs. We show that the consumed mass is dominated for the BH component with
larger initial normalization as given by the BH mass-function. Assuming that
about 10% of the tidally disrupted stars contribute in the growth of SgrA*
mass, stars make up the second dominant effect in enhancing the mass of SgrA*.
We consider the detectability of the GW signal from inspiralling stellar mass
BHs around SgrA* with LISA. Computing the fraction of the lifetime of every BH
species in the LISA band, with signal to noise ratio $\gtrsim 8$, to their
entire lifetime, and rescaling this number with the total number of BHs in the
system, we find that the total expected rate of inspirals per Milky-Way sized
galaxy per year is $10^{-5}$. Quite interestingly, the rate is dominated for
the BH component with larger initial normalization as dictated by the BH
mass-function. We interpret it as the second signature of the BH mass-function.
