Given a set B of finite rooted graphs and a radius r as an input, we prove
that it is undecidable to determine whether there exists a sequence (G_i) of
finite bounded degree graphs such that the rooted r-radius neighbourhood of a
random node of G_i is isomorphic to a rooted graph in B with probability
tending to 1. Our proof implies a similar result for the case where the
sequence (G_i) is replaced by a unimodular random graph.Comment: 6 page
