  We investigate the limit behaviour of the spectral measures of matrices
following the Gibbs measure for the Ising model on random graphs, Potts model
on random graphs, matrices coupled in a chain model or induced QCD model. For
most of these models, we prove that the spectral measures converge almost
surely and describe their limit via solutions to an Euler equation for
isentropic flow with negative pressure $p(\rho)=-3^{-1}\pi^2 \rho^3$.
