Poisson Convergence in the n-Cube

We consider two types of random subgraphs of the n-cube Q_n obtained by independent deletion the vertices (together with all edges incident with them) or the edges of Qⁿ, respectively, with a prescribed probability q = 1 — p. For these two probabilistic models we determine some values of the probability p for which the number of (isolated) k-dimensional subcubes or the number of vertices of a given degree k, respectively, has asymptotically a Poisson or a Normal distribution. The technique which will be used is that of Poisson convergence introduced by BARBOUR 1] (see also 4]).