Nonlinear stochastic biasing of beaks and halos: Scale-dependence, time-evolution, and redshift-space distortion from cosmological N-body simulations

We have quantified the degree of nonlinearity and stochasticity of the clus tering of biased objects using cosmological N-body simulations. Adopting th e peaks and the halos as representative biasing models, we focused on the t wo-point correlation of the biased objects, dark matter and their cross-cor relation. Especially. we took account of the effect of redshift-space disto rtion and attempted to clarify the scale dependence and the time dependence by analyzing the biasing factor and the cross-correlation factor, On small scales, stochasticity and nonlinearity become appreciable and strongly obj ect-dependent, especially in redshift space due to the pair-wise velocity d ispersion of the biased objects. Nevertheless, an approximation of determin istic linear biasing, delta (obj) similar or equal to b(obj)delta (mass), w orks reasonably well even in the quasi-linear regime, r greater than or sim ilar to 10 h(-1) Mpc, and linear redshift-space distortion explains the clu stering amplitudes in redshift space in this regime.