Hello,
I am looking for references/results about the following problem. Let W be a NON-symmetric adjacency matrix where the probability to have a directed edge from vertex j to vertex i decays exponentially with the distance between the two vertices. Are there known results about:
1. The probability law of the eigenvalue of largest modulus ?
2. The spectral distribution in the complex plane ?
3. Complex eigenvectors ?
I am not really expecting results for 3, but maybe there are some for 1 and 2 ?
Many thanks
Bruno Cessac