${\mathrm{\ell }}^2$-Betti numbers of random rooted simplicial complexes

We define unimodular measures on the space of rooted simplicial complexes and associate to each measure a chain complex and a trace function. As a consequence, we can define ${\mathrm{\ell }}^2$-Betti numbers of unimodular random rooted simplicial complexes and show that they are continuous under Benjamini-Schramm convergence.