Let $G$ be an Erdos-Renyi random graph (i.e. an edge ($ij$) exists with probability $0 < p < 1$ and all edges are independent). Let $L$ be the Laplacian matrix of this graph (i.e $L=D-A$, where $A$ is the adjacency matrix of the graph and $D$ is diagonal with $D_{ii} = $ degree of node $i$). Let finally $0 = \lambda_0 \leq \lambda_1 \leq \lambda_2 \leq \cdots$ be the eigenvalues of $L$. Is an analytic expression known for the limiting empirical distribution of these eigenvalues, i.e. for

$\lim_{n \to \infty} \frac{1}{n} \#\{ 1 \leq j \leq n : \lambda_j \leq t \}, t \in \mathbb{R}?$