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.
