Transition scale to a homogeneous universe

We analyze observed and simulated galaxy and cluster samples to find the transition scale to homogeneity in the real space (the correlation transition scale), r_t_, and in the Fourier space (the spectral transition scale), λ_t_. The correlation transition scale is determined by the minimum of the second derivative of the correlation function, the spectral scale by the transition from a negative to a positive spectral index. Available data suggest values r_t_ = 130 +/- 10 h^-1^ and λ_t_ = 175 +/- 15 h^-1^ Mpc. These values are in good agreement with the amplitude of fluctuations of the cosmic microwave background radiation. The comparison of potential fields of model samples of identical transition scale but different spectral index on large scales demonstrates that long-wavelength fluctuations influence significantly the potential field. Consequently the fair sample size must be larger than the spectral transition scale.