I am interested in properties of random directed graphs with fixed out-degree $d$. I am imagining a random graph model where each vertex chooses d neighbors (say, with replacement) u.a.r.
Question: Is anything known about the stationary distribution and mixing times of random walks on these random graphs (for various values of $d$)?
I am particularly interested in the case where $d = 2$, which corresponds to a model of random automata over a Boolean alphabet. (Yes, I realize these graphs are often not connected, but what happens in a given component?) I am happy with partial results and results about other properties of these graphs.
It seems most of the literature on random graphs focuses on the Erdős–Rényi model, which has very different properties than the model I am thinking about.