  We present a numerical strategy to compute ensemble averages of
coarse-grained two-dimensional membrane-like models. The approach consists in
generalizing to these two-dimensional models a one-dimensional strategy exposed
in [Blanc, Le Bris, Legoll, Patz, JNLS 2010], which is based on applying the
ergodic theorem to Markov chains. This may be considered as a first step
towards computing the constitutive law associated to such models, in the
thermodynamic limit.
