  It is crucial to understand and model a behavior of galaxy biasing for future
ambitious galaxy redshift surveys. Using 40 large cosmological N-body
simulations for a standard LambdaCDM cosmology, we study the cross-correlation
coefficient between matter and the halo density field, which is an indicator of
the stochasticity of bias, over a wide redshift range 0\le z \le 3. The
cross-correlation coefficient is important to extract information on the matter
density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing
measurements. We compare the simulation results with integrated perturbation
theory (iPT) proposed by one of the present authors and standard perturbation
theory (SPT) combined with a phenomenological model of local bias. The
cross-correlation coefficient derived from the iPT agrees with N-body
simulation results down to r~15 (10) h^{-1}Mpc within 0.5 (1.0) % for all
redshifts and halo masses we consider. The SPT with local bias does not explain
complicated behaviors on quasilinear scales at low redshifts, while roughly
reproduces the general behavior of the cross-correlation coefficient on fully
nonlinear scales. The iPT is powerful to predict the cross-correlation
coefficient down to quasilinear regimes with a high precision.
