In this talk I will introduce a recent work in which we studied the co-evolution of supermassive black holes (SMBHs) with galaxies by means of semi-analytic model (SAM) of galaxy formation. We utilized the simulation results from Guo 2013 and Henriques 2015 and studied the stochastic gravitational wave background (GWB) signal generated by SMBH mergers. We made predictions for the GWB amplitude, and studied the different galaxy merger behaviors in these two models related to their different predictions. We also calculated the spatially isotropic two point auto- and cross-correlation functions (2PCFs) for both SMBHs and galaxies by using mock catalogs, and studied their dependence on both redshift and galaxy/SMBH mass.
