Abstract : We consider a finite simplicial complex K together with its successive barycentric subdivisions Sd^d(K),d>0 and study the expected topology of a random subcomplex in Sd^d(K),d>>0. In this talk, we will present expected Euler characteristic and asymptotic upper/lower bounds for the expected Betti numbers of those subcomplexes. This is a joint work with Jean-Yves Welschinger