rooted simplicial complexes $(K,x)$, $(L,y)$ are isomorphic if there is a simplicial isomorphism $\Phi\colon K\to L$ such that $\Phi(x)=y$. Let $\mathcal{SC}_*$ be the space of *isomorphism classes of connected locally finite rooted simplicial complexes* (see Section \[rrsc\]). Bowen made use of this space in [@bowen] but similar ideas can already be found in [@elek].\
Every finite simplicial complex $K$ defines a *random rooted simplicial complex* $\mu_K$, which is a probability measure on ${\mathcal{SC}_*}$, by choosing uniformly at random a vertex $x\in V(K)$ as root (Example \[example-measures\]). A sequence $K_n$ of simplicial complexes *converges weakly* or *Benjamini-Schramm* if the measures $\mu_{K_n}$ weakly converge (Definition \[definition-BSconvergence\]). The notion of weak convergence of graphs goes back to Benjamini and Schramm [@benjamini-schramm] - for simplicial complexes it was introduced by Elek in [@elek].\
We will give a definition of $\ell^2$-Betti numbers of unimodular random rooted simplicial complexes (Definition \[bettinumbers\]) and provide a proof of the following result:

Let $(\mu_n)_{n\in{{\mathbb N}}}$ be a sequence of sofic random rooted simplicial complexes with uniformly bounded vertex degree. If the sequence weakly converge to a random rooted simplicial complex $\mu$, then the $\ell^2$-Betti numbers of $(\mu_n)_{n\in{{\mathbb N}}}$ converge to the $\ell^2$-Betti numbers of $\mu$.

As a consequence we 