Abstract
In these last two lectures, we are interested in models of random (q+1)-regular graphs with N vertices. We study the spectral hole of the adjacency matrix, in the limit where N tends to infinity. We present a result due to Joel Friedman, and several steps in its proof: with probability tending towards 1, the spectral hole is quasi-optimal, i.e. greater than (q+1)-2q^{1/2}-\epsilon.
