$r$ and all finite $[L,y]\in {\mathcal{SC}_*}$. This is equivalent to say that the [*rrsc*]{}s $\mu_{K_n}$ weakly converges to $\mu_K$ i.e. $$\int_{{\mathcal{SC}_*}} f([L,x])d\mu_{K_n}([L,x])\to \int_{{\mathcal{SC}_*}} f([L,x])d\mu_{K}([L,x])$$ for all bounded continuous functions $f\colon{\mathcal{SC}_*}\to \mathbb{R}$.

We call a random rooted simplicial complex $\mu$ *sofic* if there is a sequence $(K_n)_n$ of finite connected simplicial complexes converging Benjamini-Schramm to $\mu$.

It is clear that sofic measures are unimodular since unimodularity is preserved under weak convergence. It is an open question if all unimodular measures are sofic [@aldous-lyons].

Let $K$ be a simplicial complex of vertex degree bounded by some $D\in {{\mathbb N}}$ with a simplicial, proper and cocompact action of a discrete group $\Gamma$. Suppose that $\Gamma$ is residually finite and let $(N_n)_{n\in N}$ be a descending sequence of finite index normal subgroups of $\Gamma$ with $\bigcap_{n\in{{\mathbb N}}}N_n=\{1\}$. Then the sequence $(K_n)_n:=(K/N_n)_n$ converges Benjamini-Schramm to $$\mu_K=\frac{1}{c(\Gamma)}\sum_{x\in{\mathcal F}^{(0)}} \frac{\delta_{[K,x]}}{|{\mathrm{Stab}}_\Gamma(x)|},$$ where ${\mathcal F}$ is a fundamental domain for the $\Gamma$-action. This can be seen by the following fact: We fix an $r>0$. Then, for sufficiently large $n\in {{\mathbb N}}$, the $r$-ball $B_r(K,x)$ is isomorphic to the $r$-ball $B_r(K_n,xN_n)$ for all $x\in V(K)$ and the action of $N_n$ on $K$ is free. Let ${\mathcal F}(N_n)$ be a fundamental 