  We study numerically some discrete growth models belonging to the class of
the nonlinear molecular beam epitaxy equation, or Villain-Lai-Das Sarma (VLDS)
equation. The conserved restricted solid-on-solid model (CRSOS) with maximum
heights differences H_m=1 and H_m=2 was analyzed in substrate dimensions d=1
and d=2. The Das Sarma and Tamborenea (DT) model and a competitive model
involving random deposition and CRSOS deposition were studied in d=1. For the
CRSOS model with H_m=1 we obtain the more accurate estimates of scaling
exponents in d=1: roughness exponent alpha = 0.94 +- 0.02 and dynamical
exponent z = 2.88 +- 0.04. These estimates are significantly below the values
of one-loop renormalization for the VLDS theory, which confirms Janssen's
proposal of the existence of higher order corrections. The roughness exponent
in d=2 is very near the one-loop result alpha=2/3, in agreement with previous
works. The moments W_n of orders n=2,3,4 of the heights distribution were
calculated for all models and the skewness S = W_3/{W_2}^{3/2} and the kurtosis
Q = W_4/{W_2}^{2}-3 were estimated. At the steady states, the CRSOS models and
the competitive model have nearly the same values of S and Q in d=1, which
suggests that these amplitude ratios are universal in the VLDS class. The
estimates for the DT model are different, possibly due to their typically long
crossover to asymptotic values. Results for the CRSOS models in d=2 also
suggest that those quantities are universal.
