  Partial Bergman kernels $\Pi_{k, E}$ are kernels of orthogonal projections
onto subspaces $\mathcal{k} \subset H^0(M, L^k)$ of holomorphic sections of the
$k$th power of an ample line bundle over a Kahler manifold $(M, \omega)$. The
subspaces of this article are spectral subspaces $\{\hat{H}_k \leq E\}$ of the
Toeplitz quantization $\hat{H}_k$ of a smooth Hamiltonian $H: M \to
\mathbb{R}$. It is shown that the relative partial density of states
$\frac{\Pi_{k, E}(z)}{\Pi_k(z)} \to {1}_{\mathcal{A}}$ where $\mathcal{A} = \{H
< E\}$. Moreover it is shown that this partial density of states exhibits
`Erf'-asymptotics along the interface $\partial \mathcal{A}$, that is, the
density profile asymptotically has a Gaussian error function shape
interpolating between the values $1,0$ of ${1}_{\mathcal{A}}$. Such
`erf'-asymptotics are a universal edge effect. The different types of scaling
asymptotics are reminiscent of the law of large numbers and central limit
theorem
