  We consider a nonlinear convex stochastic homogenization problem, in a
stationary setting. In practice, the deterministic homogenized energy density
can only be approximated by a random apparent energy density, obtained by
solving the corrector problem on a truncated domain.
  We show that the technique of antithetic variables can be used to reduce the
variance of the computed quantities, and thereby decrease the computational
cost at equal accuracy. This leads to an efficient approach for approximating
expectations of the apparent homogenized energy density and of related
quantities.
  The efficiency of the approach is numerically illustrated on several test
cases. Some elements of analysis are also provided.
