05 February 2020 2 7K Report

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

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